From 8a594bb12813d3efdf39dff05e300c014ee753d2 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 14 Oct 2021 09:44:37 +0200
Subject: [PATCH 01/44] Split docs in 2 pages and add explanations

---
 docs/make.jl      |  2 +-
 docs/src/api.md   | 25 +++++++++++++++++++++++++
 docs/src/index.md | 17 +++++++++++++----
 3 files changed, 39 insertions(+), 5 deletions(-)
 create mode 100644 docs/src/api.md

diff --git a/docs/make.jl b/docs/make.jl
index 69a122c..ce790be 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -3,7 +3,7 @@ using Documenter, GPLikelihoods
 makedocs(;
     modules=[GPLikelihoods],
     format=Documenter.HTML(),
-    pages=["Home" => "index.md"],
+    pages=["Home" => "index.md", "API" => "api.md"],
     repo="https://github.com/JuliaGaussianProcesses/GPLikelihoods.jl/blob/{commit}{path}#L{line}",
     sitename="GPLikelihoods.jl",
     authors="JuliaGaussianProcesses organization",
diff --git a/docs/src/api.md b/docs/src/api.md
new file mode 100644
index 0000000..6e78d0a
--- /dev/null
+++ b/docs/src/api.md
@@ -0,0 +1,25 @@
+# API
+
+```@index
+```
+
+## Likelihoods
+
+```@docs
+BernoulliLikelihood
+CategoricalLikelihood
+ExponentialLikelihood
+GammaLikelihood
+GaussianLikelihood
+PoissonLikelihood
+```
+
+## Links
+
+```@docs
+Link
+```
+
+The rest of the links `ExpLink`, `LogisticLink`, etc., are simple aliases for the
+corresponding wrapped functions in a `Link`.
+For example `ExpLink == Link{::typeof(exp)}`.
diff --git a/docs/src/index.md b/docs/src/index.md
index b036128..064bec3 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,8 +1,17 @@
 # GPLikelihoods.jl
 
-```@index
-```
+`GPLikelihoods.jl` provides a practical interface to connect non-conjugate likelihoods
+with Gaussian Processes.
+The API is very basic, every `AbstractLikelihood` object is functor taking a 
+scalar/vector `f` and returns a `Distribution` from `Distributions.jl`. 
 
-```@autodocs
-Modules = [GPLikelihoods]
+```@doctest
+    f = 2.0
+    GaussianLikelihood()(f) == Normal(2.0)
 ```
+
+Since the parameter domain of a lot of distributions is more restricted to the real
+domain, for example the parameter of a `Bernoulli` distribution, most `AbstractLikelihood`
+contain a `invlink` field which will map the latent variable to the right domain.
+
+[`Link`](@ref)s can be created using the constructor `Link(::Function)`.
\ No newline at end of file

From 708158faf7897176cb626caee9580921c67f6e98 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 14 Oct 2021 10:19:02 +0200
Subject: [PATCH 02/44] Update docs Manifest and add some examples/tests

---
 docs/Manifest.toml | 55 ++++++++++++++++++++--------------------------
 docs/src/index.md  | 15 ++++++++++++-
 2 files changed, 38 insertions(+), 32 deletions(-)

diff --git a/docs/Manifest.toml b/docs/Manifest.toml
index b447396..f7288ca 100644
--- a/docs/Manifest.toml
+++ b/docs/Manifest.toml
@@ -1,5 +1,10 @@
 # This file is machine-generated - editing it directly is not advised
 
+[[ANSIColoredPrinters]]
+git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
+uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9"
+version = "0.0.1"
+
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
@@ -7,27 +12,23 @@ uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
-[[Distributed]]
-deps = ["Random", "Serialization", "Sockets"]
-uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
-
 [[DocStringExtensions]]
-deps = ["LibGit2", "Markdown", "Pkg", "Test"]
-git-tree-sha1 = "50ddf44c53698f5e784bbebb3f4b21c5807401b1"
+deps = ["LibGit2"]
+git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-version = "0.8.3"
+version = "0.8.5"
 
 [[Documenter]]
-deps = ["Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
-git-tree-sha1 = "c01a7e8bcf7a6693444a52a0c5ac8b4e9528600e"
+deps = ["ANSIColoredPrinters", "Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
+git-tree-sha1 = "8b43e37cfb4f4edc2b6180409acc0cebce7fede8"
 uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-version = "0.26.0"
+version = "0.27.7"
 
 [[IOCapture]]
-deps = ["Logging"]
-git-tree-sha1 = "377252859f740c217b936cebcd918a44f9b53b59"
+deps = ["Logging", "Random"]
+git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
 uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
-version = "0.1.1"
+version = "0.2.2"
 
 [[InteractiveUtils]]
 deps = ["Markdown"]
@@ -35,17 +36,14 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
-git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
+git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
-version = "0.21.1"
+version = "0.21.2"
 
 [[LibGit2]]
-deps = ["Printf"]
+deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
-[[Libdl]]
-uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
-
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
@@ -56,22 +54,21 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
+[[NetworkOptions]]
+uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
+
 [[Parsers]]
 deps = ["Dates"]
-git-tree-sha1 = "6370b5b3cf2ce5a3d2b6f7ab2dc10f374e4d7d2b"
+git-tree-sha1 = "98f59ff3639b3d9485a03a72f3ab35bab9465720"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "1.0.14"
-
-[[Pkg]]
-deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
-uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+version = "2.0.6"
 
 [[Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
 [[REPL]]
-deps = ["InteractiveUtils", "Markdown", "Sockets"]
+deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
 [[Random]]
@@ -88,12 +85,8 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
 [[Test]]
-deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
+deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
-[[UUIDs]]
-deps = ["Random", "SHA"]
-uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
-
 [[Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
diff --git a/docs/src/index.md b/docs/src/index.md
index 064bec3..4969e58 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -5,13 +5,26 @@ with Gaussian Processes.
 The API is very basic, every `AbstractLikelihood` object is functor taking a 
 scalar/vector `f` and returns a `Distribution` from `Distributions.jl`. 
 
-```@doctest
+```@jldoctest
     f = 2.0
     GaussianLikelihood()(f) == Normal(2.0)
+
+    # output
+
+    true
 ```
 
 Since the parameter domain of a lot of distributions is more restricted to the real
 domain, for example the parameter of a `Bernoulli` distribution, most `AbstractLikelihood`
 contain a `invlink` field which will map the latent variable to the right domain.
 
+```@jldoctest
+    f = 2.0
+    BernoulliLikelihood(Link(logistic))(2.0) == Bernoulli(logistic(2.0))
+
+    # output
+
+    true
+```
+
 [`Link`](@ref)s can be created using the constructor `Link(::Function)`.
\ No newline at end of file

From d18754e9223077b90dae425244d92624692f9110 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 14 Oct 2021 10:33:17 +0200
Subject: [PATCH 03/44] replace jldoctest by example

---
 docs/src/index.md | 12 ++----------
 1 file changed, 2 insertions(+), 10 deletions(-)

diff --git a/docs/src/index.md b/docs/src/index.md
index 4969e58..c9d3889 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -5,26 +5,18 @@ with Gaussian Processes.
 The API is very basic, every `AbstractLikelihood` object is functor taking a 
 scalar/vector `f` and returns a `Distribution` from `Distributions.jl`. 
 
-```@jldoctest
+```@example
     f = 2.0
     GaussianLikelihood()(f) == Normal(2.0)
-
-    # output
-
-    true
 ```
 
 Since the parameter domain of a lot of distributions is more restricted to the real
 domain, for example the parameter of a `Bernoulli` distribution, most `AbstractLikelihood`
 contain a `invlink` field which will map the latent variable to the right domain.
 
-```@jldoctest
+```@example
     f = 2.0
     BernoulliLikelihood(Link(logistic))(2.0) == Bernoulli(logistic(2.0))
-
-    # output
-
-    true
 ```
 
 [`Link`](@ref)s can be created using the constructor `Link(::Function)`.
\ No newline at end of file

From c213531322621ff346db96fbdf9e44012b726a14 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 14 Oct 2021 10:56:10 +0200
Subject: [PATCH 04/44] Add more api docs

---
 docs/src/api.md | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/docs/src/api.md b/docs/src/api.md
index 6e78d0a..38900f2 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -11,6 +11,7 @@ CategoricalLikelihood
 ExponentialLikelihood
 GammaLikelihood
 GaussianLikelihood
+HeteroscedasticGaussianLikelihood
 PoissonLikelihood
 ```
 
@@ -18,8 +19,33 @@ PoissonLikelihood
 
 ```@docs
 Link
+ChainLink
 ```
 
 The rest of the links `ExpLink`, `LogisticLink`, etc., are simple aliases for the
 corresponding wrapped functions in a `Link`.
 For example `ExpLink == Link{::typeof(exp)}`.
+
+We provide nonetheless docs for them:
+
+```@docs
+LogLink
+ExpLink
+InvLink
+SqrtLink
+SquareLink
+LogitLink
+LogisticLink
+ProbitLink
+NormalCDFLink
+SoftMaxLink
+```
+
+## Misc
+
+```@docs
+inverse
+```
+
+!!! warning 
+    This whole part might be replaced soon by the `InverseFunctions.jl` package.

From cf68d0eaa3c2b1b4661d96729abe4606a137e326 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 14 Oct 2021 14:44:13 +0200
Subject: [PATCH 05/44] Resolved comments

---
 docs/src/api.md   | 13 ++-----------
 docs/src/index.md |  4 ++--
 2 files changed, 4 insertions(+), 13 deletions(-)

diff --git a/docs/src/api.md b/docs/src/api.md
index 38900f2..6daaca5 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -24,7 +24,7 @@ ChainLink
 
 The rest of the links `ExpLink`, `LogisticLink`, etc., are simple aliases for the
 corresponding wrapped functions in a `Link`.
-For example `ExpLink == Link{::typeof(exp)}`.
+For example `ExpLink == Link{typeof(exp)}`.
 
 We provide nonetheless docs for them:
 
@@ -39,13 +39,4 @@ LogisticLink
 ProbitLink
 NormalCDFLink
 SoftMaxLink
-```
-
-## Misc
-
-```@docs
-inverse
-```
-
-!!! warning 
-    This whole part might be replaced soon by the `InverseFunctions.jl` package.
+```
\ No newline at end of file
diff --git a/docs/src/index.md b/docs/src/index.md
index c9d3889..9c263d8 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -16,7 +16,7 @@ contain a `invlink` field which will map the latent variable to the right domain
 
 ```@example
     f = 2.0
-    BernoulliLikelihood(Link(logistic))(2.0) == Bernoulli(logistic(2.0))
+    BernoulliLikelihood(logistic)(f) == Bernoulli(logistic(2.0))
 ```
 
-[`Link`](@ref)s can be created using the constructor `Link(::Function)`.
\ No newline at end of file
+[`Link`](@ref)s can be created using the constructor `Link(l)` where `l` is a function or a functor.
\ No newline at end of file

From 15fb16515120e52af2f36a9fb33d7134f73a0215 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 22 Oct 2021 11:10:49 +0200
Subject: [PATCH 06/44] Apply suggestions from code review

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>
---
 docs/src/index.md | 15 +++++++--------
 1 file changed, 7 insertions(+), 8 deletions(-)

diff --git a/docs/src/index.md b/docs/src/index.md
index 9c263d8..b804f97 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -2,21 +2,20 @@
 
 `GPLikelihoods.jl` provides a practical interface to connect non-conjugate likelihoods
 with Gaussian Processes.
-The API is very basic, every `AbstractLikelihood` object is functor taking a 
-scalar/vector `f` and returns a `Distribution` from `Distributions.jl`. 
+The API is very basic: Every `AbstractLikelihood` object is a [functor](https://docs.julialang.org/en/v1/manual/methods/#Function-like-objects-1) that takes the output of a Gaussian process as input and returns a `Distribution` from [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl). 
 
-```@example
-    f = 2.0
-    GaussianLikelihood()(f) == Normal(2.0)
+```@repl
+f = 2.0;
+GaussianLikelihood()(f) == Normal(2.0)
 ```
 
 Since the parameter domain of a lot of distributions is more restricted to the real
 domain, for example the parameter of a `Bernoulli` distribution, most `AbstractLikelihood`
 contain a `invlink` field which will map the latent variable to the right domain.
 
-```@example
-    f = 2.0
-    BernoulliLikelihood(logistic)(f) == Bernoulli(logistic(2.0))
+```@repl
+f = 2.0;
+BernoulliLikelihood(logistic)(f) == Bernoulli(logistic(2.0))
 ```
 
 [`Link`](@ref)s can be created using the constructor `Link(l)` where `l` is a function or a functor.
\ No newline at end of file

From c247484033323555eee8039dd30ea685ebc51bed Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 11 Nov 2021 23:35:00 +0100
Subject: [PATCH 07/44] Use InverseFunctions (#56)

* Use InverseFunctions

* Update Project.toml
---
 Project.toml         |  6 ++++--
 src/GPLikelihoods.jl |  4 +---
 src/inverse.jl       | 27 ---------------------------
 src/links.jl         |  6 +++---
 test/inverse.jl      | 32 --------------------------------
 test/runtests.jl     |  1 -
 6 files changed, 8 insertions(+), 68 deletions(-)
 delete mode 100644 src/inverse.jl
 delete mode 100644 test/inverse.jl

diff --git a/Project.toml b/Project.toml
index b823d6d..4a0fd4c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,11 +1,12 @@
 name = "GPLikelihoods"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
 authors = ["JuliaGaussianProcesses Team"]
-version = "0.2.4"
+version = "0.2.5"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
@@ -13,5 +14,6 @@ StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
 [compat]
 Distributions = "0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25"
 Functors = "0.1, 0.2"
-StatsFuns = "0.9"
+InverseFunctions = "0.1.2"
+StatsFuns = "0.9.13"
 julia = "1.3"
diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index df0a070..d250c04 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -2,6 +2,7 @@ module GPLikelihoods
 
 using Distributions
 using Functors
+using InverseFunctions: InverseFunctions
 using LinearAlgebra
 using Random
 using StatsFuns
@@ -26,9 +27,6 @@ export Link,
     NormalCDFLink,
     SoftMaxLink
 
-# Inverses
-include("inverse.jl")
-
 # Links
 include("links.jl")
 
diff --git a/src/inverse.jl b/src/inverse.jl
deleted file mode 100644
index 5e5f53a..0000000
--- a/src/inverse.jl
+++ /dev/null
@@ -1,27 +0,0 @@
-"""
-    inverse(f)
-
-Return the inverse of function `f`.
-
-This is an internal function to avoid type piracies such as `inv(::typeof(exp))`. At some
-point `inv` might support standard Julia functions which would allow us to remove `inverse`.
-"""
-inverse(f)
-
-inverse(::typeof(exp)) = log
-inverse(::typeof(log)) = exp
-
-inverse(::typeof(log1pexp)) = logexpm1
-inverse(::typeof(logexpm1)) = log1pexp
-
-inverse(::typeof(inv)) = inv
-
-square(x) = x^2
-inverse(::typeof(sqrt)) = square
-inverse(::typeof(square)) = sqrt
-
-inverse(::typeof(logit)) = logistic
-inverse(::typeof(logistic)) = logit
-
-inverse(::typeof(normcdf)) = norminvcdf
-inverse(::typeof(norminvcdf)) = normcdf
diff --git a/src/links.jl b/src/links.jl
index 82d0fef..d87cdc4 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -25,7 +25,7 @@ end
 
 (l::Link)(x) = l.f(x)
 
-Base.inv(l::Link) = Link(inverse(l.f))
+Base.inv(l::Link) = Link(InverseFunctions.inverse(l.f))
 
 # alias
 const LogLink = Link{typeof(log)}
@@ -34,7 +34,7 @@ const ExpLink = Link{typeof(exp)}
 const InvLink = Link{typeof(inv)}
 
 const SqrtLink = Link{typeof(sqrt)}
-const SquareLink = Link{typeof(square)}
+const SquareLink = Link{typeof(InverseFunctions.square)}
 
 const LogitLink = Link{typeof(logit)}
 const LogisticLink = Link{typeof(logistic)}
@@ -77,7 +77,7 @@ SqrtLink() = Link(sqrt)
 
 `^2` link, f:ℝ->ℝ⁺∪{0}. Its inverse is the [`SqrtLink`](@ref).
 """
-SquareLink() = Link(square)
+SquareLink() = Link(InverseFunctions.square)
 
 """
     LogitLink()
diff --git a/test/inverse.jl b/test/inverse.jl
deleted file mode 100644
index c9a4c36..0000000
--- a/test/inverse.jl
+++ /dev/null
@@ -1,32 +0,0 @@
-@testset "inverse.jl" begin
-    @testset "square" begin
-        x = randn()
-        @test GPLikelihoods.square(x) == x^2
-    end
-
-    @testset "inverse" begin
-        x = rand()
-        for f in (
-            exp,
-            log,
-            inv,
-            log1pexp,
-            logexpm1,
-            sqrt,
-            GPLikelihoods.square,
-            logit,
-            logistic,
-            normcdf,
-            norminvcdf,
-        )
-            g = GPLikelihoods.inverse(f)
-
-            # check that definitions are correct
-            @test g(f(x)) ≈ x
-            @test f(g(x)) ≈ x
-
-            # check that definitions are complete
-            @test GPLikelihoods.inverse(g) === f
-        end
-    end
-end
diff --git a/test/runtests.jl b/test/runtests.jl
index 5da718a..1679108 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -8,7 +8,6 @@ using StatsFuns
 
 @testset "GPLikelihoods.jl" begin
     include("test_utils.jl")
-    include("inverse.jl")
     include("links.jl")
     @testset "likelihoods" begin
         include("likelihoods/bernoulli.jl")

From fcdf235e18acc63575c96f749c547d501dd08170 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 16:09:55 +0100
Subject: [PATCH 08/44] Move the test interface inside of `src`

---
 src/TestInterface.jl | 66 ++++++++++++++++++++++++++++++++++++++++++++
 test/runtests.jl     |  2 +-
 test/test_utils.jl   | 51 ----------------------------------
 3 files changed, 67 insertions(+), 52 deletions(-)
 create mode 100644 src/TestInterface.jl
 delete mode 100644 test/test_utils.jl

diff --git a/src/TestInterface.jl b/src/TestInterface.jl
new file mode 100644
index 0000000..623496a
--- /dev/null
+++ b/src/TestInterface.jl
@@ -0,0 +1,66 @@
+module TestInterface
+
+using Random
+
+export test_inferface
+
+function test_interface(
+rng::AbstractRNG, lik, kernel, x::AbstractVector; functor_args=()
+)
+gp = GP(kernel)
+lgp = LatentGP(gp, lik, 1e-5)
+lfgp = lgp(x)
+
+# Check if likelihood produces a distribution
+@test lik(rand(rng, lfgp.fx)) isa Distribution
+
+N = length(x)
+y = rand(rng, lfgp.fx)
+
+if x isa MOInput
+    # TODO: replace with mo_inverse_transform
+    N = length(x.x)
+    y = [y[[i + j * N for j in 0:(x.out_dim - 1)]] for i in 1:N]
+end
+
+# Check if the likelihood samples are of correct length
+@test length(rand(rng, lik(y))) == N
+
+# Check if functor works properly
+xs, re = Functors.functor(lik)
+@test lik == re(xs)
+if isempty(functor_args)
+    @test xs === ()
+else
+    @test keys(xs) == functor_args
+end
+
+return nothing
+end
+
+@doc raw"""
+    test_interface([rng::AbstractRNG,] lik, k::Kernel, x::AbstractVector; functor_args=())
+
+!!! warning
+
+    KernelFunctions.jl and AbstractGPs.jl need to be loaded in the current workspace
+    to run this function.
+
+This function provides unified method to check the interface of the various likelihoods 
+defined. It checks if the likelihood produces a distribution, length of likelihood 
+samples is correct and if the functor works as intended.
+
+...
+# Arguments
+- `lik`: the likelihood to test the interface of
+- `k::Kernel`: the kernel to use for the GP
+- `x::AbstractVector`: inputs to compute the likelihood on
+- `functor_args=()`: a collection of symbols of arguments to match functor parameters with.
+...
+"""
+function test_interface(lik, kernel, x::AbstractVector; kwargs...)
+    return test_interface(Random.GLOBAL_RNG, lik, k, x; kwargs...)
+end
+
+
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 1679108..a465a16 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,4 +1,5 @@
 using GPLikelihoods
+using GPLikelihoods.TestInterface
 using AbstractGPs
 using Test
 using Random
@@ -7,7 +8,6 @@ using Distributions
 using StatsFuns
 
 @testset "GPLikelihoods.jl" begin
-    include("test_utils.jl")
     include("links.jl")
     @testset "likelihoods" begin
         include("likelihoods/bernoulli.jl")
diff --git a/test/test_utils.jl b/test/test_utils.jl
deleted file mode 100644
index 02f72cf..0000000
--- a/test/test_utils.jl
+++ /dev/null
@@ -1,51 +0,0 @@
-function test_interface(
-    rng::AbstractRNG, lik, k::Kernel, x::AbstractVector; functor_args=()
-)
-    gp = GP(k)
-    lgp = LatentGP(gp, lik, 1e-5)
-    lfgp = lgp(x)
-
-    # Check if likelihood produces a distribution
-    @test lik(rand(rng, lfgp.fx)) isa Distribution
-
-    N = length(x)
-    y = rand(rng, lfgp.fx)
-
-    if x isa MOInput
-        # TODO: replace with mo_inverse_transform
-        N = length(x.x)
-        y = [y[[i + j * N for j in 0:(x.out_dim - 1)]] for i in 1:N]
-    end
-
-    # Check if the likelihood samples are of correct length
-    @test length(rand(rng, lik(y))) == N
-
-    # Check if functor works properly
-    xs, re = Functors.functor(lik)
-    @test lik == re(xs)
-    if isempty(functor_args)
-        @test xs === ()
-    else
-        @test keys(xs) == functor_args
-    end
-
-    return nothing
-end
-
-"""
-    test_interface(lik, k::Kernel, x::AbstractVector; functor_args=())
-
-This function provides unified method to check the interface of the various likelihoods 
-defined. It checks if the likelihood produces a distribution, length of likelihood 
-samples is correct and if the functor works as intended.  
-...
-# Arguments
-- `lik`: the likelihood to test the interface of
-- `k::Kernel`: the kernel to use for the GP
-- `x::AbstractVector`: intputs to compute the likelihood on
-- `functor_args=()`: a collection of symbols of arguments to match functor parameters with.
-...
-"""
-function test_interface(lik, k::KernelFunctions.Kernel, x::AbstractVector; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, lik, k, x; kwargs...)
-end

From 37bae37639c6bb5ec93f3e535f19d8fdb7be0c57 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 16:25:59 +0100
Subject: [PATCH 09/44] Remove docs/Manifest from tracked files

---
 docs/Manifest.toml | 99 ----------------------------------------------
 1 file changed, 99 deletions(-)
 delete mode 100644 docs/Manifest.toml

diff --git a/docs/Manifest.toml b/docs/Manifest.toml
deleted file mode 100644
index b447396..0000000
--- a/docs/Manifest.toml
+++ /dev/null
@@ -1,99 +0,0 @@
-# This file is machine-generated - editing it directly is not advised
-
-[[Base64]]
-uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
-
-[[Dates]]
-deps = ["Printf"]
-uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
-
-[[Distributed]]
-deps = ["Random", "Serialization", "Sockets"]
-uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
-
-[[DocStringExtensions]]
-deps = ["LibGit2", "Markdown", "Pkg", "Test"]
-git-tree-sha1 = "50ddf44c53698f5e784bbebb3f4b21c5807401b1"
-uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-version = "0.8.3"
-
-[[Documenter]]
-deps = ["Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
-git-tree-sha1 = "c01a7e8bcf7a6693444a52a0c5ac8b4e9528600e"
-uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-version = "0.26.0"
-
-[[IOCapture]]
-deps = ["Logging"]
-git-tree-sha1 = "377252859f740c217b936cebcd918a44f9b53b59"
-uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
-version = "0.1.1"
-
-[[InteractiveUtils]]
-deps = ["Markdown"]
-uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
-
-[[JSON]]
-deps = ["Dates", "Mmap", "Parsers", "Unicode"]
-git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
-uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
-version = "0.21.1"
-
-[[LibGit2]]
-deps = ["Printf"]
-uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
-
-[[Libdl]]
-uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
-
-[[Logging]]
-uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
-
-[[Markdown]]
-deps = ["Base64"]
-uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
-
-[[Mmap]]
-uuid = "a63ad114-7e13-5084-954f-fe012c677804"
-
-[[Parsers]]
-deps = ["Dates"]
-git-tree-sha1 = "6370b5b3cf2ce5a3d2b6f7ab2dc10f374e4d7d2b"
-uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "1.0.14"
-
-[[Pkg]]
-deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
-uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-
-[[Printf]]
-deps = ["Unicode"]
-uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
-
-[[REPL]]
-deps = ["InteractiveUtils", "Markdown", "Sockets"]
-uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
-
-[[Random]]
-deps = ["Serialization"]
-uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-
-[[SHA]]
-uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
-
-[[Serialization]]
-uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
-
-[[Sockets]]
-uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
-
-[[Test]]
-deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
-uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[[UUIDs]]
-deps = ["Random", "SHA"]
-uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
-
-[[Unicode]]
-uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

From c745fc07a1cdf9a727acfecd7e8a5264017e3990 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 16:51:21 +0100
Subject: [PATCH 10/44] Move things around

---
 .gitignore           | 1 +
 Project.toml         | 5 +++--
 src/GPLikelihoods.jl | 3 +++
 src/TestInterface.jl | 5 ++---
 test/runtests.jl     | 2 +-
 5 files changed, 10 insertions(+), 6 deletions(-)

diff --git a/.gitignore b/.gitignore
index a22e235..f4f2fb4 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,6 +4,7 @@
 .DS_Store
 /Manifest.toml
 test/Manifest.toml
+docs/Manifest.toml
 /dev/
 /docs/build/
 /docs/site/
diff --git a/Project.toml b/Project.toml
index 4a0fd4c..4b8f7dd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "GPLikelihoods"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
 authors = ["JuliaGaussianProcesses Team"]
-version = "0.2.5"
+version = "0.2.6"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
@@ -10,10 +10,11 @@ InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 Distributions = "0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25"
 Functors = "0.1, 0.2"
 InverseFunctions = "0.1.2"
-StatsFuns = "0.9.13"
+StatsFuns = "0.9"
 julia = "1.3"
diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index d250c04..1640577 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -39,4 +39,7 @@ include("likelihoods/poisson.jl")
 include("likelihoods/gamma.jl")
 include("likelihoods/exponential.jl")
 
+# TestInterface module
+include("TestInterface.jl")
+
 end # module
diff --git a/src/TestInterface.jl b/src/TestInterface.jl
index 623496a..25b0bbb 100644
--- a/src/TestInterface.jl
+++ b/src/TestInterface.jl
@@ -1,8 +1,7 @@
 module TestInterface
 
 using Random
-
-export test_inferface
+using Test
 
 function test_interface(
 rng::AbstractRNG, lik, kernel, x::AbstractVector; functor_args=()
@@ -59,7 +58,7 @@ samples is correct and if the functor works as intended.
 ...
 """
 function test_interface(lik, kernel, x::AbstractVector; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, lik, k, x; kwargs...)
+    return test_interface(Random.GLOBAL_RNG, lik, kernel, x; kwargs...)
 end
 
 
diff --git a/test/runtests.jl b/test/runtests.jl
index a465a16..6be558a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,5 +1,5 @@
 using GPLikelihoods
-using GPLikelihoods.TestInterface
+using GPLikelihoods.TestInterface: test_interface
 using AbstractGPs
 using Test
 using Random

From 8f997913a90336447d4571ccddaf0ee1df448535 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 17:20:16 +0100
Subject: [PATCH 11/44] Make docs more explicit

---
 docs/src/api.md   |  9 ++++++---
 docs/src/index.md | 33 ++++++++++++++++++++++++---------
 2 files changed, 30 insertions(+), 12 deletions(-)

diff --git a/docs/src/api.md b/docs/src/api.md
index 6daaca5..13b6ca2 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -22,11 +22,14 @@ Link
 ChainLink
 ```
 
-The rest of the links `ExpLink`, `LogisticLink`, etc., are simple aliases for the
-corresponding wrapped functions in a `Link`.
+The rest of the links [`ExpLink`](@ref), [`LogisticLink`](@ref), etc.,
+are aliases for the corresponding wrapped functions in a `Link`.
 For example `ExpLink == Link{typeof(exp)}`.
 
-We provide nonetheless docs for them:
+When passing a [`Link`](@ref) to an `AbstractLikelihood`, that this link 
+corresponds to the transformation `p=link(f)` while, as mentioned in the
+[`Constrained parameters`](@ref) section, the statistics literature usually use
+ the denomination [**inverse link or mean function**](https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function) for it.
 
 ```@docs
 LogLink
diff --git a/docs/src/index.md b/docs/src/index.md
index b804f97..e7d7b32 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,21 +1,36 @@
-# GPLikelihoods.jl
+```@meta
+CurrentModule = GPLikelihoods
+```
+# GPLikelihoods
 
-`GPLikelihoods.jl` provides a practical interface to connect non-conjugate likelihoods
+[`GPLikelihoods.jl`](https://github.com/JuliaGaussianProcesses/GPLikelihoods.jl) provides a practical interface to connect non-conjugate likelihoods
 with Gaussian Processes.
-The API is very basic: Every `AbstractLikelihood` object is a [functor](https://docs.julialang.org/en/v1/manual/methods/#Function-like-objects-1) that takes the output of a Gaussian process as input and returns a `Distribution` from [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl). 
+The API is very basic: Every `AbstractLikelihood` object is a [functor](https://docs.julialang.org/en/v1/manual/methods/#Function-like-objects-1)
+that takes the output of a Gaussian process as input and returns a 
+`Distribution` from [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl). 
 
 ```@repl
 f = 2.0;
 GaussianLikelihood()(f) == Normal(2.0)
 ```
 
-Since the parameter domain of a lot of distributions is more restricted to the real
-domain, for example the parameter of a `Bernoulli` distribution, most `AbstractLikelihood`
-contain a `invlink` field which will map the latent variable to the right domain.
+### Constrained parameters
+
+The domain of some distributions parameters can be different from 
+``\mathbb{R}``, the real domain.
+To solve this problem, we also provide the [`Link`](@ref) type, which can be
+passed to the [`Likelihood`](@ref) constructors.
+Alternatively, `function`s can also directly be passed and will be wrapped in a `Link`).
+For more details about which likelihoods require a [`Link`](@ref) check out their docs.
+We typically named this passed link as the `invlink`.
+This comes from the  statistic literature, where the "link" is defined as `f = link(y)`.
+
+A classical example is the [`BernoulliLikelihood`](@ref) for classification, with the probability parameter ``p \in \[0, 1\]``.
+The default it to use a [`logistic`](https://en.wikipedia.org/wiki/Logistic_function) transformation, but one could also use the inverse of the [`probit`](https://en.wikipedia.org/wiki/Probit) link:
 
 ```@repl
 f = 2.0;
-BernoulliLikelihood(logistic)(f) == Bernoulli(logistic(2.0))
+BernoulliLikelihood()(f) == Bernoulli(logistic(f))
+BernoulliLikelihood(NormalCDFLink()) == Bernoulli(normalcdf(f))
 ```
-
-[`Link`](@ref)s can be created using the constructor `Link(l)` where `l` is a function or a functor.
\ No newline at end of file
+Note that we passed the `inverse` of the `probit` function which is the `normalcdf` function.
\ No newline at end of file

From ce81e7b5e7607ec1002119e8d58ea56b8271aca5 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 17:25:56 +0100
Subject: [PATCH 12/44] Saved current version of TestInterface

---
 src/TestInterface.jl          |  7 ++--
 test/TestInterface.jl.save    | 65 +++++++++++++++++++++++++++++++++++
 test/likelihoods/bernoulli.jl |  2 +-
 3 files changed, 68 insertions(+), 6 deletions(-)
 create mode 100644 test/TestInterface.jl.save

diff --git a/src/TestInterface.jl b/src/TestInterface.jl
index 25b0bbb..51b8167 100644
--- a/src/TestInterface.jl
+++ b/src/TestInterface.jl
@@ -4,14 +4,11 @@ using Random
 using Test
 
 function test_interface(
-rng::AbstractRNG, lik, kernel, x::AbstractVector; functor_args=()
+rng::AbstractRNG, lik, D_in=1; functor_args=()
 )
-gp = GP(kernel)
-lgp = LatentGP(gp, lik, 1e-5)
-lfgp = lgp(x)
 
 # Check if likelihood produces a distribution
-@test lik(rand(rng, lfgp.fx)) isa Distribution
+@test lik(rand(rng, )) isa Distribution
 
 N = length(x)
 y = rand(rng, lfgp.fx)
diff --git a/test/TestInterface.jl.save b/test/TestInterface.jl.save
new file mode 100644
index 0000000..0d8a17d
--- /dev/null
+++ b/test/TestInterface.jl.save
@@ -0,0 +1,65 @@
+module TestInterface
+
+using Random
+using Test
+
+function test_interface(
+rng::AbstractRNG, lik, x::AbstractVector; functor_args=()
+)
+gp = GP(kernel)
+lgp = LatentGP(gp, lik, 1e-5)
+lfgp = lgp(x)
+
+# Check if likelihood produces a distribution
+@test lik(rand(rng, lfgp.fx)) isa Distribution
+
+N = length(x)
+y = rand(rng, lfgp.fx)
+
+if x isa MOInput
+    # TODO: replace with mo_inverse_transform
+    N = length(x.x)
+    y = [y[[i + j * N for j in 0:(x.out_dim - 1)]] for i in 1:N]
+end
+
+# Check if the likelihood samples are of correct length
+@test length(rand(rng, lik(y))) == N
+
+# Check if functor works properly
+xs, re = Functors.functor(lik)
+@test lik == re(xs)
+if isempty(functor_args)
+    @test xs === ()
+else
+    @test keys(xs) == functor_args
+end
+
+return nothing
+end
+
+@doc raw"""
+    test_interface([rng::AbstractRNG,] lik, k::Kernel, x::AbstractVector; functor_args=())
+
+!!! warning
+
+    KernelFunctions.jl and AbstractGPs.jl need to be loaded in the current workspace
+    to run this function.
+
+This function provides unified method to check the interface of the various likelihoods 
+defined. It checks if the likelihood produces a distribution, length of likelihood 
+samples is correct and if the functor works as intended.
+
+...
+# Arguments
+- `lik`: the likelihood to test the interface of
+- `k::Kernel`: the kernel to use for the GP
+- `x::AbstractVector`: inputs to compute the likelihood on
+- `functor_args=()`: a collection of symbols of arguments to match functor parameters with.
+...
+"""
+function test_interface(lik, kernel, x::AbstractVector; kwargs...)
+    return test_interface(Random.GLOBAL_RNG, lik, kernel, x; kwargs...)
+end
+
+
+end
\ No newline at end of file
diff --git a/test/likelihoods/bernoulli.jl b/test/likelihoods/bernoulli.jl
index 4cc2039..4905ac4 100644
--- a/test/likelihoods/bernoulli.jl
+++ b/test/likelihoods/bernoulli.jl
@@ -4,5 +4,5 @@
     end
 
     lik = BernoulliLikelihood()
-    test_interface(lik, SqExponentialKernel(), rand(10))
+    test_interface(lik)
 end

From a72eacefbdc1d5b7046bbd50449c4076d029fd31 Mon Sep 17 00:00:00 2001
From: Theo Galy-Fajou <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 17:48:58 +0100
Subject: [PATCH 13/44] Simplified the tests

---
 src/TestInterface.jl            | 84 ++++++++++++++++-----------------
 test/Project.toml               |  2 -
 test/likelihoods/bernoulli.jl   |  2 +-
 test/likelihoods/categorical.jl |  8 ++--
 test/likelihoods/exponential.jl |  2 +-
 test/likelihoods/gamma.jl       |  2 +-
 test/likelihoods/gaussian.jl    |  6 +--
 test/likelihoods/poisson.jl     |  2 +-
 test/runtests.jl                |  1 -
 9 files changed, 52 insertions(+), 57 deletions(-)

diff --git a/src/TestInterface.jl b/src/TestInterface.jl
index 51b8167..4556ec3 100644
--- a/src/TestInterface.jl
+++ b/src/TestInterface.jl
@@ -1,62 +1,60 @@
 module TestInterface
 
+using Functors
 using Random
 using Test
 
-function test_interface(
-rng::AbstractRNG, lik, D_in=1; functor_args=()
-)
-
-# Check if likelihood produces a distribution
-@test lik(rand(rng, )) isa Distribution
-
-N = length(x)
-y = rand(rng, lfgp.fx)
-
-if x isa MOInput
-    # TODO: replace with mo_inverse_transform
-    N = length(x.x)
-    y = [y[[i + j * N for j in 0:(x.out_dim - 1)]] for i in 1:N]
-end
-
-# Check if the likelihood samples are of correct length
-@test length(rand(rng, lik(y))) == N
-
-# Check if functor works properly
-xs, re = Functors.functor(lik)
-@test lik == re(xs)
-if isempty(functor_args)
-    @test xs === ()
-else
-    @test keys(xs) == functor_args
-end
-
-return nothing
+function test_interface(rng::AbstractRNG, lik, out_dist, D_in=1; functor_args=())
+    N = 10
+    T = Float64 # TODO test Float32 as well
+    f, fs = if D_in == 1
+        f = randn(rng, T)
+        fs = randn(rng, T, 10)
+        f, fs
+    else
+        f = randn(rng, T, D_in)
+        fs = [randn(rng, T, D_in) for _ in 1:N]
+        f, fs
+    end
+    # Check if likelihood produces the correct distribution
+    # and is sampleable
+    @test lik(f) isa out_dist
+    @test_nowarn rand(rng, lik(f))
+
+    # Check if the likelihood samples are of correct length
+    @test length(rand(rng, lik(fs))) == N
+
+    # Check if functor works properly
+    xs, re = Functors.functor(lik)
+    @test lik == re(xs)
+    if isempty(functor_args)
+        @test xs === ()
+    else
+        @test keys(xs) == functor_args
+    end
+
+    return nothing
 end
 
 @doc raw"""
-    test_interface([rng::AbstractRNG,] lik, k::Kernel, x::AbstractVector; functor_args=())
-
-!!! warning
-
-    KernelFunctions.jl and AbstractGPs.jl need to be loaded in the current workspace
-    to run this function.
+    test_interface([rng::AbstractRNG,] lik, out_dist; functor_args=())
 
 This function provides unified method to check the interface of the various likelihoods 
-defined. It checks if the likelihood produces a distribution, length of likelihood 
+defined. It checks if the likelihood produces the correct distribution, length of likelihood 
 samples is correct and if the functor works as intended.
 
 ...
-# Arguments
+## Arguments
 - `lik`: the likelihood to test the interface of
-- `k::Kernel`: the kernel to use for the GP
-- `x::AbstractVector`: inputs to compute the likelihood on
+- `out_dist::Type{<:Distribution}`: the type of distribution the likelihood should return
+- `D_in::Int=1` : The input dimension of the likelihood
+
+## Keyword arguments
 - `functor_args=()`: a collection of symbols of arguments to match functor parameters with.
 ...
 """
-function test_interface(lik, kernel, x::AbstractVector; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, lik, kernel, x; kwargs...)
+function test_interface(lik, out_dist, D_in=1; kwargs...)
+    return test_interface(Random.GLOBAL_RNG, lik, out_dist, D_in; kwargs...)
 end
 
-
-end
\ No newline at end of file
+end
diff --git a/test/Project.toml b/test/Project.toml
index bccaf0a..259ad91 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,5 +1,4 @@
 [deps]
-AbstractGPs = "99985d1d-32ba-4be9-9821-2ec096f28918"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -7,7 +6,6 @@ StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-AbstractGPs = "0.2, 0.3, 0.4, 0.5"
 Distributions = "0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25"
 Functors = "0.1, 0.2"
 StatsFuns = "0.9"
diff --git a/test/likelihoods/bernoulli.jl b/test/likelihoods/bernoulli.jl
index 4905ac4..d9a9b28 100644
--- a/test/likelihoods/bernoulli.jl
+++ b/test/likelihoods/bernoulli.jl
@@ -4,5 +4,5 @@
     end
 
     lik = BernoulliLikelihood()
-    test_interface(lik)
+    test_interface(lik, Bernoulli)
 end
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index 042c1e6..ed5184f 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -4,9 +4,9 @@
     end
 
     lik = CategoricalLikelihood()
-    IN_DIM = 3
+    # IN_DIM = 3
     OUT_DIM = 4
-    N = 10
-    X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
-    test_interface(lik, IndependentMOKernel(SqExponentialKernel()), X)
+    # N = 10
+    # X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
+    test_interface(lik, Categorical, OUT_DIM)
 end
diff --git a/test/likelihoods/exponential.jl b/test/likelihoods/exponential.jl
index 7b3c383..4fd9ea8 100644
--- a/test/likelihoods/exponential.jl
+++ b/test/likelihoods/exponential.jl
@@ -4,5 +4,5 @@
     end
 
     lik = ExponentialLikelihood()
-    test_interface(lik, SqExponentialKernel(), rand(10))
+    test_interface(lik, Exponential)
 end
diff --git a/test/likelihoods/gamma.jl b/test/likelihoods/gamma.jl
index 05c7ca9..1c5141e 100644
--- a/test/likelihoods/gamma.jl
+++ b/test/likelihoods/gamma.jl
@@ -6,5 +6,5 @@
     end
 
     lik = GammaLikelihood(1.0)
-    test_interface(lik, SqExponentialKernel(), rand(10); functor_args=(:α, :invlink))
+    test_interface(lik, Gamma; functor_args=(:α, :invlink))
 end
diff --git a/test/likelihoods/gaussian.jl b/test/likelihoods/gaussian.jl
index 53ad0ed..79c964e 100644
--- a/test/likelihoods/gaussian.jl
+++ b/test/likelihoods/gaussian.jl
@@ -1,6 +1,6 @@
 @testset "GaussianLikelihood" begin
     lik = GaussianLikelihood(1e-5)
-    test_interface(lik, SqExponentialKernel(), rand(10); functor_args=(:σ²,))
+    test_interface(lik, Normal; functor_args=(:σ²,))
 end
 
 @testset "HeteroscedasticGaussianLikelihood" begin
@@ -13,6 +13,6 @@ end
     IN_DIM = 3
     OUT_DIM = 2 # one for the mean the other for the log-standard deviation
     N = 10
-    X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
-    test_interface(lik, IndependentMOKernel(SqExponentialKernel()), X)
+    # X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
+    test_interface(lik, Normal, 2)
 end
diff --git a/test/likelihoods/poisson.jl b/test/likelihoods/poisson.jl
index a5d00a5..9369e94 100644
--- a/test/likelihoods/poisson.jl
+++ b/test/likelihoods/poisson.jl
@@ -4,6 +4,6 @@
     end
 
     for lik in (PoissonLikelihood(), PoissonLikelihood(log1pexp))
-        test_interface(lik, SqExponentialKernel(), rand(10))
+        test_interface(lik, Poisson)
     end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 6be558a..1d6735b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,5 @@
 using GPLikelihoods
 using GPLikelihoods.TestInterface: test_interface
-using AbstractGPs
 using Test
 using Random
 using Functors

From fb7544bdcf6e0f45b7da8a124fa9e573bc554d21 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 16 Dec 2021 18:08:20 +0100
Subject: [PATCH 14/44] Revert compat StatsFuns

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 4b8f7dd..7e9bece 100644
--- a/Project.toml
+++ b/Project.toml
@@ -16,5 +16,5 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Distributions = "0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25"
 Functors = "0.1, 0.2"
 InverseFunctions = "0.1.2"
-StatsFuns = "0.9"
+StatsFuns = "0.9.13"
 julia = "1.3"

From 587ee76d4882d45603e38c23e9fe6772407a08b2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Mon, 20 Dec 2021 17:18:34 +0100
Subject: [PATCH 15/44] Delete TestInterface.jl.save

---
 test/TestInterface.jl.save | 65 --------------------------------------
 1 file changed, 65 deletions(-)
 delete mode 100644 test/TestInterface.jl.save

diff --git a/test/TestInterface.jl.save b/test/TestInterface.jl.save
deleted file mode 100644
index 0d8a17d..0000000
--- a/test/TestInterface.jl.save
+++ /dev/null
@@ -1,65 +0,0 @@
-module TestInterface
-
-using Random
-using Test
-
-function test_interface(
-rng::AbstractRNG, lik, x::AbstractVector; functor_args=()
-)
-gp = GP(kernel)
-lgp = LatentGP(gp, lik, 1e-5)
-lfgp = lgp(x)
-
-# Check if likelihood produces a distribution
-@test lik(rand(rng, lfgp.fx)) isa Distribution
-
-N = length(x)
-y = rand(rng, lfgp.fx)
-
-if x isa MOInput
-    # TODO: replace with mo_inverse_transform
-    N = length(x.x)
-    y = [y[[i + j * N for j in 0:(x.out_dim - 1)]] for i in 1:N]
-end
-
-# Check if the likelihood samples are of correct length
-@test length(rand(rng, lik(y))) == N
-
-# Check if functor works properly
-xs, re = Functors.functor(lik)
-@test lik == re(xs)
-if isempty(functor_args)
-    @test xs === ()
-else
-    @test keys(xs) == functor_args
-end
-
-return nothing
-end
-
-@doc raw"""
-    test_interface([rng::AbstractRNG,] lik, k::Kernel, x::AbstractVector; functor_args=())
-
-!!! warning
-
-    KernelFunctions.jl and AbstractGPs.jl need to be loaded in the current workspace
-    to run this function.
-
-This function provides unified method to check the interface of the various likelihoods 
-defined. It checks if the likelihood produces a distribution, length of likelihood 
-samples is correct and if the functor works as intended.
-
-...
-# Arguments
-- `lik`: the likelihood to test the interface of
-- `k::Kernel`: the kernel to use for the GP
-- `x::AbstractVector`: inputs to compute the likelihood on
-- `functor_args=()`: a collection of symbols of arguments to match functor parameters with.
-...
-"""
-function test_interface(lik, kernel, x::AbstractVector; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, lik, kernel, x; kwargs...)
-end
-
-
-end
\ No newline at end of file

From 5e3aa5b0de6bbaef743b24fddbd74308336faee6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 4 Jan 2022 13:52:48 +0100
Subject: [PATCH 16/44] Tidying up

Co-authored-by: willtebbutt <wct23@cam.ac.uk>
---
 test/likelihoods/categorical.jl | 3 ---
 test/likelihoods/gaussian.jl    | 1 -
 2 files changed, 4 deletions(-)

diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index ed5184f..b129a24 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -4,9 +4,6 @@
     end
 
     lik = CategoricalLikelihood()
-    # IN_DIM = 3
     OUT_DIM = 4
-    # N = 10
-    # X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
     test_interface(lik, Categorical, OUT_DIM)
 end
diff --git a/test/likelihoods/gaussian.jl b/test/likelihoods/gaussian.jl
index 79c964e..fe9f210 100644
--- a/test/likelihoods/gaussian.jl
+++ b/test/likelihoods/gaussian.jl
@@ -13,6 +13,5 @@ end
     IN_DIM = 3
     OUT_DIM = 2 # one for the mean the other for the log-standard deviation
     N = 10
-    # X = MOInput([rand(IN_DIM) for _ in 1:N], OUT_DIM)
     test_interface(lik, Normal, 2)
 end

From 0d624816fb9caee322d2e9a473814a3925ecc876 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 4 Jan 2022 14:09:47 +0100
Subject: [PATCH 17/44] Delete Manifest.toml

---
 docs/Manifest.toml | 92 ----------------------------------------------
 1 file changed, 92 deletions(-)
 delete mode 100644 docs/Manifest.toml

diff --git a/docs/Manifest.toml b/docs/Manifest.toml
deleted file mode 100644
index f7288ca..0000000
--- a/docs/Manifest.toml
+++ /dev/null
@@ -1,92 +0,0 @@
-# This file is machine-generated - editing it directly is not advised
-
-[[ANSIColoredPrinters]]
-git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
-uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9"
-version = "0.0.1"
-
-[[Base64]]
-uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
-
-[[Dates]]
-deps = ["Printf"]
-uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
-
-[[DocStringExtensions]]
-deps = ["LibGit2"]
-git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
-uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-version = "0.8.5"
-
-[[Documenter]]
-deps = ["ANSIColoredPrinters", "Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
-git-tree-sha1 = "8b43e37cfb4f4edc2b6180409acc0cebce7fede8"
-uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-version = "0.27.7"
-
-[[IOCapture]]
-deps = ["Logging", "Random"]
-git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
-uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
-version = "0.2.2"
-
-[[InteractiveUtils]]
-deps = ["Markdown"]
-uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
-
-[[JSON]]
-deps = ["Dates", "Mmap", "Parsers", "Unicode"]
-git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
-uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
-version = "0.21.2"
-
-[[LibGit2]]
-deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
-uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
-
-[[Logging]]
-uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
-
-[[Markdown]]
-deps = ["Base64"]
-uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
-
-[[Mmap]]
-uuid = "a63ad114-7e13-5084-954f-fe012c677804"
-
-[[NetworkOptions]]
-uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
-
-[[Parsers]]
-deps = ["Dates"]
-git-tree-sha1 = "98f59ff3639b3d9485a03a72f3ab35bab9465720"
-uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "2.0.6"
-
-[[Printf]]
-deps = ["Unicode"]
-uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
-
-[[REPL]]
-deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
-uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
-
-[[Random]]
-deps = ["Serialization"]
-uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-
-[[SHA]]
-uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
-
-[[Serialization]]
-uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
-
-[[Sockets]]
-uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
-
-[[Test]]
-deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
-uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[[Unicode]]
-uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

From f10bd3eb90cff691ed10757a066feb092368733a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 4 Jan 2022 14:24:05 +0100
Subject: [PATCH 18/44] Update docs/src/api.md

Co-authored-by: willtebbutt <wct23@cam.ac.uk>
---
 docs/src/api.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/api.md b/docs/src/api.md
index 13b6ca2..48ec7ce 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -26,7 +26,7 @@ The rest of the links [`ExpLink`](@ref), [`LogisticLink`](@ref), etc.,
 are aliases for the corresponding wrapped functions in a `Link`.
 For example `ExpLink == Link{typeof(exp)}`.
 
-When passing a [`Link`](@ref) to an `AbstractLikelihood`, that this link 
+When passing a [`Link`](@ref) to an `AbstractLikelihood`, this link 
 corresponds to the transformation `p=link(f)` while, as mentioned in the
 [`Constrained parameters`](@ref) section, the statistics literature usually use
  the denomination [**inverse link or mean function**](https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function) for it.

From f00d7b229adff76af9481da53f137c4f8365ffc0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 4 Jan 2022 14:45:12 +0100
Subject: [PATCH 19/44] Explain single-latent vs multi-latent

---
 docs/src/index.md | 29 ++++++++++++++++++++++++-----
 1 file changed, 24 insertions(+), 5 deletions(-)

diff --git a/docs/src/index.md b/docs/src/index.md
index e7d7b32..3b20c05 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -3,15 +3,34 @@ CurrentModule = GPLikelihoods
 ```
 # GPLikelihoods
 
-[`GPLikelihoods.jl`](https://github.com/JuliaGaussianProcesses/GPLikelihoods.jl) provides a practical interface to connect non-conjugate likelihoods
-with Gaussian Processes.
+[`GPLikelihoods.jl`](https://github.com/JuliaGaussianProcesses/GPLikelihoods.jl) provides a practical interface to connect Gaussian and non-conjugate likelihoods
+to Gaussian Processes.
 The API is very basic: Every `AbstractLikelihood` object is a [functor](https://docs.julialang.org/en/v1/manual/methods/#Function-like-objects-1)
-that takes the output of a Gaussian process as input and returns a 
-`Distribution` from [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl). 
+taking a `Real` or an `AbstractVector` as an input and returns a 
+`Distribution` from [`Distributions.jl`](https://github.com/JuliaStats/Distributions.jl).
 
+### Single-latent vs multi-latent likelihoods
+
+Most likelihoods, like the [`GaussianLikelihood`](@ref), only require one latent Gaussian process.
+Passing a `Real` will therefore return a [`UnivariateDistribution`](https://juliastats.org/Distributions.jl/latest/univariate/),
+and passing an `AbstractVector{<:Real}` will return a [multivariate product of distributions](https://juliastats.org/Distributions.jl/latest/multivariate/#Product-distributions).
 ```@repl
 f = 2.0;
 GaussianLikelihood()(f) == Normal(2.0)
+fs = [2.0, 3.0, 1.5]
+GaussianLikelihood()(fs) == Product([Normal(2.0), Normal(3.0), Normal(1.5)])
+```
+
+Some likelihoods, like the [`CategoricalLikelihood`](@ref), requires multiple latent Gaussian processes,
+and an `AbstractVector{<:Real}` needs to be passed.
+To obtain a product of distributions an `AbstractVector{<:AbstractVector{<:Real}}` has to be passed (we recommend
+using [`ColVecs` and `RowVecs` from KernelFunctions.jl](https://juliagaussianprocesses.github.io/KernelFunctions.jl/stable/api/#Vector-Valued-Inputs)
+if you need to transform an `AbstractMatrix`).
+```@repl
+fs = [2.0, 3.0, 4.5];
+CategoricalLikelihood()(fs) isa Categorical
+Fs = [rand(3) for _ in 1:4] 
+CategoricalLikelihood()(Fs) isa Product{<:Any,<:Categorical}
 ```
 
 ### Constrained parameters
@@ -33,4 +52,4 @@ f = 2.0;
 BernoulliLikelihood()(f) == Bernoulli(logistic(f))
 BernoulliLikelihood(NormalCDFLink()) == Bernoulli(normalcdf(f))
 ```
-Note that we passed the `inverse` of the `probit` function which is the `normalcdf` function.
\ No newline at end of file
+Note that we passed the `inverse` of the `probit` function which is the `normalcdf` function.

From 0ad840f84ac6c0a8272e8792c2452af7cf3cbfc6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 15:34:36 +0100
Subject: [PATCH 20/44] Rework categorical to allow multiple variants

---
 Project.toml                   |  2 +-
 src/GPLikelihoods.jl           |  2 ++
 src/likelihoods/categorical.jl | 34 ++++++++++++++++++++++++++++------
 3 files changed, 31 insertions(+), 7 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7e9bece..f069172 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "GPLikelihoods"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
 authors = ["JuliaGaussianProcesses Team"]
-version = "0.2.6"
+version = "0.2.7"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 1640577..4e4079c 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -14,6 +14,8 @@ export BernoulliLikelihood,
     PoissonLikelihood,
     ExponentialLikelihood,
     GammaLikelihood
+export SimplexVariant,
+    CurvedVariant
 export Link,
     ChainLink,
     ExpLink,
diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 9756c0d..0a98d4b 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -1,22 +1,44 @@
+struct SimplexVariant end
+
+struct CurvedVariant end
+
 """
-    CategoricalLikelihood(l=softmax)
+    CategoricalLikelihood(l=softmax, variant=SimplexVariant())
 
 Categorical likelihood is to be used if we assume that the 
-uncertainity associated with the data follows a Categorical distribution.
+uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) with `n` categories.
 ```math
     p(y|f_1, f_2, \\dots, f_{n-1}) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_{n-1}, 0))
+    p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
 ```
+Two variants are possible:
+## `SimplexVariant`
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n-1}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n-1}, 0)``.
+It is used by default.
+
+## `CurvedVariant`
+Given an `AbstractVector` ``[f_1, f_2, ..., f_{n}]``, returns a `Categorical` distribution,
+with probabilities given by ``l(f_1, f_2, ..., f_{n})``.
+The "Curved" comes from the fact that such a distribution is "curved exponential family"
+as there are `n-1` independent parameters embedded in a `n` dimensional parameter space.
+A lot of standard results for exponential families do not apply.
+For more explanations, see this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions) at the end of the section.
+Use with caution!
 """
-struct CategoricalLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
+struct CategoricalLikelihood{Tl<:AbstractLink,Tv} <: AbstractLikelihood
     invlink::Tl
+    variant::Tv
 end
 
-CategoricalLikelihood(l=softmax) = CategoricalLikelihood(Link(l))
+CategoricalLikelihood(l=softmax, variant=SimplexVariant()) = CategoricalLikelihood(Link(l), variant)
 
-(l::CategoricalLikelihood)(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
+(l::CategoricalLikelihood{<:AbstractLink,SimplexVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
+(l::CategoricalLikelihood{<:AbstractLink,CurvedVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(f))
 
-function (l::CategoricalLikelihood)(fs::AbstractVector)
+function (l::CategoricalLikelihood{<:AbstractLink,SimplexVariant})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(vcat.(fs, 0))))
 end
+function (l::CategoricalLikelihood{<:AbstractLink,CurvedVariant})(fs::AbstractVector)
+    return Product(Categorical.(l.invlink.(fs)))
+end
\ No newline at end of file

From 846187208067a7cf3d8af2af1e08b73aba16af6c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 15:41:04 +0100
Subject: [PATCH 21/44] Rework the constructor

---
 src/likelihoods/categorical.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 0a98d4b..2aef714 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -26,12 +26,12 @@ A lot of standard results for exponential families do not apply.
 For more explanations, see this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions) at the end of the section.
 Use with caution!
 """
-struct CategoricalLikelihood{Tl<:AbstractLink,Tv} <: AbstractLikelihood
+struct CategoricalLikelihood{Tv,Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
-    variant::Tv
+    CategoricalLikelihood{Tv}(invlink::Tl) where {Tv,Tl} = new{Tv,Tl}(invlink)
 end
 
-CategoricalLikelihood(l=softmax, variant=SimplexVariant()) = CategoricalLikelihood(Link(l), variant)
+CategoricalLikelihood(l=softmax, variant=SimplexVariant()) = CategoricalLikelihood{typeof(variant)}(Link(l))
 
 (l::CategoricalLikelihood{<:AbstractLink,SimplexVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
 (l::CategoricalLikelihood{<:AbstractLink,CurvedVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(f))

From 0ac79c24483e143071df12197781520861ab5809 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 16:21:33 +0100
Subject: [PATCH 22/44] Correct functions and add tests

---
 src/likelihoods/categorical.jl  | 8 ++++----
 test/likelihoods/categorical.jl | 7 +++++--
 2 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 2aef714..03de1eb 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -33,12 +33,12 @@ end
 
 CategoricalLikelihood(l=softmax, variant=SimplexVariant()) = CategoricalLikelihood{typeof(variant)}(Link(l))
 
-(l::CategoricalLikelihood{<:AbstractLink,SimplexVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
-(l::CategoricalLikelihood{<:AbstractLink,CurvedVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(f))
+(l::CategoricalLikelihood{SimplexVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
+(l::CategoricalLikelihood{CurvedVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(f))
 
-function (l::CategoricalLikelihood{<:AbstractLink,SimplexVariant})(fs::AbstractVector)
+function (l::CategoricalLikelihood{SimplexVariant})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(vcat.(fs, 0))))
 end
-function (l::CategoricalLikelihood{<:AbstractLink,CurvedVariant})(fs::AbstractVector)
+function (l::CategoricalLikelihood{CurvedVariant})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(fs)))
 end
\ No newline at end of file
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index b129a24..a89f4d4 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,9 +1,12 @@
 @testset "CategoricalLikelihood" begin
     for args in ((), (softmax,), (SoftMaxLink(),))
-        @test CategoricalLikelihood(args...) isa CategoricalLikelihood{SoftMaxLink}
+        @test CategoricalLikelihood(args...) isa CategoricalLikelihood{SimplexVariant,SoftMaxLink}
     end
+    @test CategoricalLikelihood(softmax, CurvedVariant()) isa CategoricalLikelihood{CurvedVariant,SoftMaxLink}
 
-    lik = CategoricalLikelihood()
+    lik_simplex = CategoricalLikelihood()
     OUT_DIM = 4
     test_interface(lik, Categorical, OUT_DIM)
+    lik_curved = CategoricalLikelihood(softmax, CurvedVariant())
+    test_interface(lik, Categorical, OUT_DIM)
 end

From ec10c5e9dd37aff8a5416adb9e7769bcdffc1170 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 16:22:12 +0100
Subject: [PATCH 23/44] Formatting

---
 src/GPLikelihoods.jl            |  3 +--
 src/likelihoods/categorical.jl  | 14 ++++++++++----
 test/likelihoods/categorical.jl |  6 ++++--
 3 files changed, 15 insertions(+), 8 deletions(-)

diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 4e4079c..1e0bea5 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -14,8 +14,7 @@ export BernoulliLikelihood,
     PoissonLikelihood,
     ExponentialLikelihood,
     GammaLikelihood
-export SimplexVariant,
-    CurvedVariant
+export SimplexVariant, CurvedVariant
 export Link,
     ChainLink,
     ExpLink,
diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 03de1eb..0627395 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -31,14 +31,20 @@ struct CategoricalLikelihood{Tv,Tl<:AbstractLink} <: AbstractLikelihood
     CategoricalLikelihood{Tv}(invlink::Tl) where {Tv,Tl} = new{Tv,Tl}(invlink)
 end
 
-CategoricalLikelihood(l=softmax, variant=SimplexVariant()) = CategoricalLikelihood{typeof(variant)}(Link(l))
+function CategoricalLikelihood(l=softmax, variant=SimplexVariant())
+    return CategoricalLikelihood{typeof(variant)}(Link(l))
+end
 
-(l::CategoricalLikelihood{SimplexVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
-(l::CategoricalLikelihood{CurvedVariant})(f::AbstractVector{<:Real}) = Categorical(l.invlink(f))
+function (l::CategoricalLikelihood{SimplexVariant})(f::AbstractVector{<:Real})
+    return Categorical(l.invlink(vcat(f, 0)))
+end
+function (l::CategoricalLikelihood{CurvedVariant})(f::AbstractVector{<:Real})
+    return Categorical(l.invlink(f))
+end
 
 function (l::CategoricalLikelihood{SimplexVariant})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(vcat.(fs, 0))))
 end
 function (l::CategoricalLikelihood{CurvedVariant})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(fs)))
-end
\ No newline at end of file
+end
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index a89f4d4..a71d6da 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,8 +1,10 @@
 @testset "CategoricalLikelihood" begin
     for args in ((), (softmax,), (SoftMaxLink(),))
-        @test CategoricalLikelihood(args...) isa CategoricalLikelihood{SimplexVariant,SoftMaxLink}
+        @test CategoricalLikelihood(args...) isa
+            CategoricalLikelihood{SimplexVariant,SoftMaxLink}
     end
-    @test CategoricalLikelihood(softmax, CurvedVariant()) isa CategoricalLikelihood{CurvedVariant,SoftMaxLink}
+    @test CategoricalLikelihood(softmax, CurvedVariant()) isa
+        CategoricalLikelihood{CurvedVariant,SoftMaxLink}
 
     lik_simplex = CategoricalLikelihood()
     OUT_DIM = 4

From 44a1f01f3ea2d1670cb7147a9f9250986deac747 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 17:22:25 +0100
Subject: [PATCH 24/44] Readapt naming

---
 src/GPLikelihoods.jl            |  1 -
 src/likelihoods/categorical.jl  | 35 ++++++++++++++-------------------
 test/likelihoods/categorical.jl | 16 +++++++--------
 3 files changed, 23 insertions(+), 29 deletions(-)

diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 1e0bea5..1640577 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -14,7 +14,6 @@ export BernoulliLikelihood,
     PoissonLikelihood,
     ExponentialLikelihood,
     GammaLikelihood
-export SimplexVariant, CurvedVariant
 export Link,
     ChainLink,
     ExpLink,
diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 0627395..f949e97 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -1,9 +1,5 @@
-struct SimplexVariant end
-
-struct CurvedVariant end
-
 """
-    CategoricalLikelihood(l=softmax, variant=SimplexVariant())
+    CategoricalLikelihood(l=softmax, bijective=true)::CategoricalLikelihood{bijective,typeof(Link(k))}
 
 Categorical likelihood is to be used if we assume that the 
 uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) with `n` categories.
@@ -12,39 +8,38 @@ uncertainty associated with the data follows a [Categorical distribution](https:
     p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
 ```
 Two variants are possible:
-## `SimplexVariant`
+## `bijective=true`
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n-1}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n-1}, 0)``.
 It is used by default.
 
-## `CurvedVariant`
+## `bijective=false`
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n})``.
-The "Curved" comes from the fact that such a distribution is "curved exponential family"
-as there are `n-1` independent parameters embedded in a `n` dimensional parameter space.
-A lot of standard results for exponential families do not apply.
-For more explanations, see this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions) at the end of the section.
-Use with caution!
+This variant is over-parametrized, as there are `n-1` independent parameters 
+embedded in a `n` dimensional parameter space.
+For more details, see the end of the section of this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions)
+where it corresponds to Variant 1 and 2.
 """
-struct CategoricalLikelihood{Tv,Tl<:AbstractLink} <: AbstractLikelihood
+struct CategoricalLikelihood{Tb,Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
-    CategoricalLikelihood{Tv}(invlink::Tl) where {Tv,Tl} = new{Tv,Tl}(invlink)
+    CategoricalLikelihood{Tb}(invlink::Tl) where {Tb,Tl} = new{Tb,Tl}(invlink)
 end
 
-function CategoricalLikelihood(l=softmax, variant=SimplexVariant())
-    return CategoricalLikelihood{typeof(variant)}(Link(l))
+function CategoricalLikelihood(l=softmax, bijective=true)
+    return CategoricalLikelihood{bijective}(Link(l))
 end
 
-function (l::CategoricalLikelihood{SimplexVariant})(f::AbstractVector{<:Real})
+function (l::CategoricalLikelihood{true})(f::AbstractVector{<:Real})
     return Categorical(l.invlink(vcat(f, 0)))
 end
-function (l::CategoricalLikelihood{CurvedVariant})(f::AbstractVector{<:Real})
+function (l::CategoricalLikelihood{false})(f::AbstractVector{<:Real})
     return Categorical(l.invlink(f))
 end
 
-function (l::CategoricalLikelihood{SimplexVariant})(fs::AbstractVector)
+function (l::CategoricalLikelihood{true})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(vcat.(fs, 0))))
 end
-function (l::CategoricalLikelihood{CurvedVariant})(fs::AbstractVector)
+function (l::CategoricalLikelihood{false})(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(fs)))
 end
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index a71d6da..d966692 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,14 +1,14 @@
 @testset "CategoricalLikelihood" begin
-    for args in ((), (softmax,), (SoftMaxLink(),))
+    for args in ((), (softmax,), (softmax, true), (SoftMaxLink(),))
         @test CategoricalLikelihood(args...) isa
-            CategoricalLikelihood{SimplexVariant,SoftMaxLink}
+            CategoricalLikelihood{true,SoftMaxLink}
     end
-    @test CategoricalLikelihood(softmax, CurvedVariant()) isa
-        CategoricalLikelihood{CurvedVariant,SoftMaxLink}
+    @test CategoricalLikelihood(softmax, false) isa
+        CategoricalLikelihood{false,SoftMaxLink}
 
-    lik_simplex = CategoricalLikelihood()
+    lik_bijective = CategoricalLikelihood()
     OUT_DIM = 4
-    test_interface(lik, Categorical, OUT_DIM)
-    lik_curved = CategoricalLikelihood(softmax, CurvedVariant())
-    test_interface(lik, Categorical, OUT_DIM)
+    test_interface(lik_bijective, Categorical, OUT_DIM)
+    lik_nonbijective = CategoricalLikelihood(softmax, false)
+    test_interface(lik_nonbijective, Categorical, OUT_DIM)
 end

From f79136b107a8ed450adaf37a899d8633d136b660 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 17:22:45 +0100
Subject: [PATCH 25/44] Formatting

---
 test/likelihoods/categorical.jl | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index d966692..5af2bee 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,10 +1,8 @@
 @testset "CategoricalLikelihood" begin
     for args in ((), (softmax,), (softmax, true), (SoftMaxLink(),))
-        @test CategoricalLikelihood(args...) isa
-            CategoricalLikelihood{true,SoftMaxLink}
+        @test CategoricalLikelihood(args...) isa CategoricalLikelihood{true,SoftMaxLink}
     end
-    @test CategoricalLikelihood(softmax, false) isa
-        CategoricalLikelihood{false,SoftMaxLink}
+    @test CategoricalLikelihood(softmax, false) isa CategoricalLikelihood{false,SoftMaxLink}
 
     lik_bijective = CategoricalLikelihood()
     OUT_DIM = 4

From e3d79dbe5c19e09a11667c5ac6277c742296cbd2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 17:45:31 +0100
Subject: [PATCH 26/44] Missing default constructor

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index f069172..47459d2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "GPLikelihoods"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
 authors = ["JuliaGaussianProcesses Team"]
-version = "0.2.7"
+version = "0.3.0"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"

From 8b076ba18747c2d9c9f51ed0eae6c13eaf318038 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 17:45:48 +0100
Subject: [PATCH 27/44] Missing function definition

---
 src/likelihoods/categorical.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index f949e97..5812623 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -30,6 +30,8 @@ function CategoricalLikelihood(l=softmax, bijective=true)
     return CategoricalLikelihood{bijective}(Link(l))
 end
 
+CategoricalLikelihood(l::AbstractLink, bijective=true) = CategoricalLikelihood{bijective}(l)
+
 function (l::CategoricalLikelihood{true})(f::AbstractVector{<:Real})
     return Categorical(l.invlink(vcat(f, 0)))
 end

From ba7ec3b02b6fffd13b42a10268bf4d57408954f5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 18:11:19 +0100
Subject: [PATCH 28/44] Applied suggestions

---
 src/likelihoods/categorical.jl  | 17 ++++++++++-------
 test/likelihoods/categorical.jl | 18 ++++++++++++++----
 2 files changed, 24 insertions(+), 11 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 5812623..7977ab6 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -1,5 +1,5 @@
 """
-    CategoricalLikelihood(l=softmax, bijective=true)::CategoricalLikelihood{bijective,typeof(Link(k))}
+    CategoricalLikelihood(l=softmax; bijective::Union{Bool,Val{false},Val{true}}=Val(true))
 
 Categorical likelihood is to be used if we assume that the 
 uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) with `n` categories.
@@ -7,8 +7,9 @@ uncertainty associated with the data follows a [Categorical distribution](https:
     p(y|f_1, f_2, \\dots, f_{n-1}) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_{n-1}, 0))
     p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
 ```
-Two variants are possible:
-## `bijective=true`
+Two variants are possible (you can use a `Bool` or `Val{true}`/`Val{false}` but
+we recommend the latter for type stability).
+## `bijective=true/Val{true}`
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n-1}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n-1}, 0)``.
 It is used by default.
@@ -23,14 +24,16 @@ where it corresponds to Variant 1 and 2.
 """
 struct CategoricalLikelihood{Tb,Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
-    CategoricalLikelihood{Tb}(invlink::Tl) where {Tb,Tl} = new{Tb,Tl}(invlink)
+    CategoricalLikelihood{Tb}(invlink) where {Tb} = CategoricalLikelihood{Tb}(Link(invlink))
+    CategoricalLikelihood{Tb}(invlink::Tl) where {Tb,Tl<:AbstractLink} = new{Tb,Tl}(invlink)
 end
 
-function CategoricalLikelihood(l=softmax, bijective=true)
-    return CategoricalLikelihood{bijective}(Link(l))
+function CategoricalLikelihood(l=softmax; bijective::Union{Bool,Val{true},Val{false}}=Val(true))
+    CategoricalLikelihood{bijective_typeparameter(bijective)}(l)
 end
 
-CategoricalLikelihood(l::AbstractLink, bijective=true) = CategoricalLikelihood{bijective}(l)
+bijective_typeparameter(bijective::Bool) = bijective
+bijective_typeparameter(::Val{T}) = T
 
 function (l::CategoricalLikelihood{true})(f::AbstractVector{<:Real})
     return Categorical(l.invlink(vcat(f, 0)))
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index 5af2bee..dbf8271 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,8 +1,18 @@
 @testset "CategoricalLikelihood" begin
-    for args in ((), (softmax,), (softmax, true), (SoftMaxLink(),))
-        @test CategoricalLikelihood(args...) isa CategoricalLikelihood{true,SoftMaxLink}
-    end
-    @test CategoricalLikelihood(softmax, false) isa CategoricalLikelihood{false,SoftMaxLink}
+    Catbij = CategoricalLikelihood{true,SoftMaxLink}
+    @test CategoricalLikelihood() isa Catbij
+    @test CategoricalLikelihood(; bijective=true) isa Catbij
+    @test CategoricalLikelihood(softmax) isa Catbij
+    @test CategoricalLikelihood(SoftMaxLink()) isa Catbij
+    @test CategoricalLikelihood(softmax; bijective=true) isa Catbij
+    @test CategoricalLikelihood(SoftMaxLink(); bijective=true) isa Catbij
+    
+    Catnonbij = CategoricalLikelihood{false,SoftMaxLink}
+    @test CategoricalLikelihood(;bijective=false) isa Catnonbij
+    @test CategoricalLikelihood(softmax; bijective=false) isa Catnonbij
+    @test CategoricalLikelihood(SoftMaxLink(); bijective=false) isa Catnonbij
+    @test CategoricalLikelihood(softmax; bijective=Val(false)) isa Catnonbij
+    @test CategoricalLikelihood(SoftMaxLink(); bijective=Val(false)) isa Catnonbij
 
     lik_bijective = CategoricalLikelihood()
     OUT_DIM = 4

From 2743debdbc9e5346eae3123d23955b7424dc8ded Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 18:12:04 +0100
Subject: [PATCH 29/44] formatting

---
 src/likelihoods/categorical.jl  | 6 ++++--
 test/likelihoods/categorical.jl | 4 ++--
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 7977ab6..a50d47b 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -28,8 +28,10 @@ struct CategoricalLikelihood{Tb,Tl<:AbstractLink} <: AbstractLikelihood
     CategoricalLikelihood{Tb}(invlink::Tl) where {Tb,Tl<:AbstractLink} = new{Tb,Tl}(invlink)
 end
 
-function CategoricalLikelihood(l=softmax; bijective::Union{Bool,Val{true},Val{false}}=Val(true))
-    CategoricalLikelihood{bijective_typeparameter(bijective)}(l)
+function CategoricalLikelihood(
+    l=softmax; bijective::Union{Bool,Val{true},Val{false}}=Val(true)
+)
+    return CategoricalLikelihood{bijective_typeparameter(bijective)}(l)
 end
 
 bijective_typeparameter(bijective::Bool) = bijective
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index dbf8271..8764b48 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -6,9 +6,9 @@
     @test CategoricalLikelihood(SoftMaxLink()) isa Catbij
     @test CategoricalLikelihood(softmax; bijective=true) isa Catbij
     @test CategoricalLikelihood(SoftMaxLink(); bijective=true) isa Catbij
-    
+
     Catnonbij = CategoricalLikelihood{false,SoftMaxLink}
-    @test CategoricalLikelihood(;bijective=false) isa Catnonbij
+    @test CategoricalLikelihood(; bijective=false) isa Catnonbij
     @test CategoricalLikelihood(softmax; bijective=false) isa Catnonbij
     @test CategoricalLikelihood(SoftMaxLink(); bijective=false) isa Catnonbij
     @test CategoricalLikelihood(softmax; bijective=Val(false)) isa Catnonbij

From ef2cc88ad7d449229b88544638de4043f1d4076d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 18:24:37 +0100
Subject: [PATCH 30/44] Missing where{T}

---
 src/likelihoods/categorical.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index a50d47b..b3edca6 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -35,7 +35,7 @@ function CategoricalLikelihood(
 end
 
 bijective_typeparameter(bijective::Bool) = bijective
-bijective_typeparameter(::Val{T}) = T
+bijective_typeparameter(::Val{T}) where {T} = T
 
 function (l::CategoricalLikelihood{true})(f::AbstractVector{<:Real})
     return Categorical(l.invlink(vcat(f, 0)))

From 1eb0f8236628ebffae2c29dffb0d42a30b3f7ee9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Thu, 27 Jan 2022 18:37:29 +0100
Subject: [PATCH 31/44] Fix test

---
 test/likelihoods/categorical.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index 8764b48..93a6c11 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -17,6 +17,6 @@
     lik_bijective = CategoricalLikelihood()
     OUT_DIM = 4
     test_interface(lik_bijective, Categorical, OUT_DIM)
-    lik_nonbijective = CategoricalLikelihood(softmax, false)
+    lik_nonbijective = CategoricalLikelihood(softmax; bijective=Val(false))
     test_interface(lik_nonbijective, Categorical, OUT_DIM)
 end

From 891916f2187446ce806994b3f6a1363ac7a385a0 Mon Sep 17 00:00:00 2001
From: Simone Surace <simone.surace@artificialy.com>
Date: Fri, 28 Jan 2022 11:18:54 +0100
Subject: [PATCH 32/44] Correct typo in `LogisticLink` docstring

---
 src/links.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/links.jl b/src/links.jl
index d87cdc4..ce2a8e9 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -89,7 +89,7 @@ LogitLink() = Link(logit)
 """
     LogisticLink()
 
-`exp(x)/(1+exp(-x))` link. f:ℝ->[0,1]. Its inverse is the [`LogitLink`](@ref).
+`1/(1+exp(-x))` link. f:ℝ->[0,1]. Its inverse is the [`LogitLink`](@ref).
 """
 LogisticLink() = Link(logistic)
 

From 63a4fd27845676b885819393a68919c3ed773461 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 11:28:13 +0100
Subject: [PATCH 33/44] Add inference tests

---
 test/likelihoods/categorical.jl | 29 +++++++++++++++++------------
 1 file changed, 17 insertions(+), 12 deletions(-)

diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index 93a6c11..b09c103 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,21 +1,26 @@
 @testset "CategoricalLikelihood" begin
     Catbij = CategoricalLikelihood{true,SoftMaxLink}
-    @test CategoricalLikelihood() isa Catbij
-    @test CategoricalLikelihood(; bijective=true) isa Catbij
-    @test CategoricalLikelihood(softmax) isa Catbij
-    @test CategoricalLikelihood(SoftMaxLink()) isa Catbij
-    @test CategoricalLikelihood(softmax; bijective=true) isa Catbij
-    @test CategoricalLikelihood(SoftMaxLink(); bijective=true) isa Catbij
+    for args in ((), (softmax,), (SoftMaxLink(),)),
+        kwargs in ((), (; bijective=true), (; bijective=Val(true)))
+
+        @test CategoricalLikelihood(args...; kwargs...) isa Catbij
+        if kwargs != (; bijective=true) # Inferred does not pass with Bool keyword
+            @inferred CategoricalLikelihood(args...; kwargs...)
+        end
+    end
 
     Catnonbij = CategoricalLikelihood{false,SoftMaxLink}
-    @test CategoricalLikelihood(; bijective=false) isa Catnonbij
-    @test CategoricalLikelihood(softmax; bijective=false) isa Catnonbij
-    @test CategoricalLikelihood(SoftMaxLink(); bijective=false) isa Catnonbij
-    @test CategoricalLikelihood(softmax; bijective=Val(false)) isa Catnonbij
-    @test CategoricalLikelihood(SoftMaxLink(); bijective=Val(false)) isa Catnonbij
+    for args in ((), (softmax,), (SoftMaxLink(),)),
+        kwargs in ((; bijective=false), (; bijective=Val(false)))
+
+        @test CategoricalLikelihood(args...; kwargs...) isa Catnonbij
+        if kwargs != (; bijective=false) # Inferred does not pass with Bool keyword
+            @inferred CategoricalLikelihood(args...; kwargs...)
+        end
+    end
 
-    lik_bijective = CategoricalLikelihood()
     OUT_DIM = 4
+    lik_bijective = CategoricalLikelihood()
     test_interface(lik_bijective, Categorical, OUT_DIM)
     lik_nonbijective = CategoricalLikelihood(softmax; bijective=Val(false))
     test_interface(lik_nonbijective, Categorical, OUT_DIM)

From c5135d8f9a2d1e27e1a07d7fc0e01ff1a03e5de6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 13:31:48 +0100
Subject: [PATCH 34/44] Update links.jl

---
 src/links.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/src/links.jl b/src/links.jl
index ce2a8e9..b8e8812 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -23,6 +23,9 @@ struct Link{F} <: AbstractLink
     f::F
 end
 
+link(f) = Link{typeof(f)}(f)
+link(l::AbstractLink) = l
+
 (l::Link)(x) = l.f(x)
 
 Base.inv(l::Link) = Link(InverseFunctions.inverse(l.f))

From b934d2927c8cb519e6f9fb2e8f7da75dfd68206e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 13:36:14 +0100
Subject: [PATCH 35/44] Use smart constructor `link` to avoid overwrapping

---
 src/GPLikelihoods.jl           | 1 +
 src/likelihoods/bernoulli.jl   | 2 +-
 src/likelihoods/categorical.jl | 2 +-
 src/likelihoods/exponential.jl | 2 +-
 src/likelihoods/gamma.jl       | 2 +-
 src/likelihoods/gaussian.jl    | 2 +-
 src/likelihoods/poisson.jl     | 2 +-
 src/links.jl                   | 2 +-
 test/links.jl                  | 5 ++++-
 9 files changed, 12 insertions(+), 8 deletions(-)

diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 1640577..0ce8099 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -14,6 +14,7 @@ export BernoulliLikelihood,
     PoissonLikelihood,
     ExponentialLikelihood,
     GammaLikelihood
+export link
 export Link,
     ChainLink,
     ExpLink,
diff --git a/src/likelihoods/bernoulli.jl b/src/likelihoods/bernoulli.jl
index a7f50c0..3866cb5 100644
--- a/src/likelihoods/bernoulli.jl
+++ b/src/likelihoods/bernoulli.jl
@@ -14,7 +14,7 @@ struct BernoulliLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
 end
 
-BernoulliLikelihood(l=logistic) = BernoulliLikelihood(Link(l))
+BernoulliLikelihood(l=logistic) = BernoulliLikelihood(link(l))
 
 (l::BernoulliLikelihood)(f::Real) = Bernoulli(l.invlink(f))
 
diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 9756c0d..7126ec1 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -13,7 +13,7 @@ struct CategoricalLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
 end
 
-CategoricalLikelihood(l=softmax) = CategoricalLikelihood(Link(l))
+CategoricalLikelihood(l=softmax) = CategoricalLikelihood(link(l))
 
 (l::CategoricalLikelihood)(f::AbstractVector{<:Real}) = Categorical(l.invlink(vcat(f, 0)))
 
diff --git a/src/likelihoods/exponential.jl b/src/likelihoods/exponential.jl
index b568db4..fdfacb8 100644
--- a/src/likelihoods/exponential.jl
+++ b/src/likelihoods/exponential.jl
@@ -11,7 +11,7 @@ struct ExponentialLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
 end
 
-ExponentialLikelihood(l=exp) = ExponentialLikelihood(Link(l))
+ExponentialLikelihood(l=exp) = ExponentialLikelihood(link(l))
 
 (l::ExponentialLikelihood)(f::Real) = Exponential(l.invlink(f))
 
diff --git a/src/likelihoods/gamma.jl b/src/likelihoods/gamma.jl
index f3a07c2..bf632d4 100644
--- a/src/likelihoods/gamma.jl
+++ b/src/likelihoods/gamma.jl
@@ -14,7 +14,7 @@ struct GammaLikelihood{T<:Real,Tl<:AbstractLink} <: AbstractLikelihood
 end
 
 GammaLikelihood(l) = GammaLikelihood(1.0, l)
-GammaLikelihood(α::Real=1.0, l=exp) = GammaLikelihood(α, Link(l))
+GammaLikelihood(α::Real=1.0, l=exp) = GammaLikelihood(α, link(l))
 
 @functor GammaLikelihood
 
diff --git a/src/likelihoods/gaussian.jl b/src/likelihoods/gaussian.jl
index 771aaec..a20fa26 100644
--- a/src/likelihoods/gaussian.jl
+++ b/src/likelihoods/gaussian.jl
@@ -40,7 +40,7 @@ struct HeteroscedasticGaussianLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
 end
 
-HeteroscedasticGaussianLikelihood(l=exp) = HeteroscedasticGaussianLikelihood(Link(l))
+HeteroscedasticGaussianLikelihood(l=exp) = HeteroscedasticGaussianLikelihood(link(l))
 
 function (l::HeteroscedasticGaussianLikelihood)(f::AbstractVector{<:Real})
     return Normal(f[1], sqrt(l.invlink(f[2])))
diff --git a/src/likelihoods/poisson.jl b/src/likelihoods/poisson.jl
index 3fcc397..c8f7e28 100644
--- a/src/likelihoods/poisson.jl
+++ b/src/likelihoods/poisson.jl
@@ -14,7 +14,7 @@ struct PoissonLikelihood{L<:AbstractLink} <: AbstractLikelihood
     invlink::L
 end
 
-PoissonLikelihood(l=exp) = PoissonLikelihood(Link(l))
+PoissonLikelihood(l=exp) = PoissonLikelihood(link(l))
 
 (l::PoissonLikelihood)(f::Real) = Poisson(l.invlink(f))
 
diff --git a/src/links.jl b/src/links.jl
index b8e8812..1e86a99 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -23,7 +23,7 @@ struct Link{F} <: AbstractLink
     f::F
 end
 
-link(f) = Link{typeof(f)}(f)
+link(f) = Link(f)
 link(l::AbstractLink) = l
 
 (l::Link)(x) = l.f(x)
diff --git a/test/links.jl b/test/links.jl
index d4e4aa2..7a70028 100644
--- a/test/links.jl
+++ b/test/links.jl
@@ -4,8 +4,11 @@
 
     # Generic link
     f = sin
-    l = Link(f)
+    l = link(f)
+    @test l == Link(f)
     @test l(x) == f(x)
+    l = link(ExpLink())
+    @test l == ExpLink()
 
     # Log
     l = LogLink()

From 4422035e812cb858cc963ab7bd949e53b904d40e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 14:31:05 +0100
Subject: [PATCH 36/44] Update src/GPLikelihoods.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>
---
 src/GPLikelihoods.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 0ce8099..1640577 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -14,7 +14,6 @@ export BernoulliLikelihood,
     PoissonLikelihood,
     ExponentialLikelihood,
     GammaLikelihood
-export link
 export Link,
     ChainLink,
     ExpLink,

From bd0c938afd89bb5dab6523ea3ebe8628ee71a803 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 14:33:40 +0100
Subject: [PATCH 37/44] Update links.jl

---
 test/links.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/links.jl b/test/links.jl
index 7a70028..b527a39 100644
--- a/test/links.jl
+++ b/test/links.jl
@@ -4,10 +4,10 @@
 
     # Generic link
     f = sin
-    l = link(f)
+    l = GPLikelihoods.link(f)
     @test l == Link(f)
     @test l(x) == f(x)
-    l = link(ExpLink())
+    l = GPLikelihoods.link(ExpLink())
     @test l == ExpLink()
 
     # Log

From c5f738773a212d2f2e12abcc11eaea8dd9362a25 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 14:45:29 +0100
Subject: [PATCH 38/44] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 7e9bece..f069172 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "GPLikelihoods"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
 authors = ["JuliaGaussianProcesses Team"]
-version = "0.2.6"
+version = "0.2.7"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"

From 7dfe9022f36d977a588cce4f76623359f1f728b5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:01:03 +0100
Subject: [PATCH 39/44] Refactoring of the formulation of the Categorical

---
 src/likelihoods/categorical.jl  | 19 ++++---------------
 src/links.jl                    | 22 ++++++++++++++++++++++
 test/likelihoods/categorical.jl |  4 ++--
 test/links.jl                   |  8 ++++++++
 4 files changed, 36 insertions(+), 17 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index b3edca6..f0e717c 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -22,31 +22,20 @@ embedded in a `n` dimensional parameter space.
 For more details, see the end of the section of this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions)
 where it corresponds to Variant 1 and 2.
 """
-struct CategoricalLikelihood{Tb,Tl<:AbstractLink} <: AbstractLikelihood
+struct CategoricalLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
-    CategoricalLikelihood{Tb}(invlink) where {Tb} = CategoricalLikelihood{Tb}(Link(invlink))
-    CategoricalLikelihood{Tb}(invlink::Tl) where {Tb,Tl<:AbstractLink} = new{Tb,Tl}(invlink)
 end
 
 function CategoricalLikelihood(
     l=softmax; bijective::Union{Bool,Val{true},Val{false}}=Val(true)
 )
-    return CategoricalLikelihood{bijective_typeparameter(bijective)}(l)
+    return CategoricalLikelihood(make_bijective(link(l), bijective))
 end
 
-bijective_typeparameter(bijective::Bool) = bijective
-bijective_typeparameter(::Val{T}) where {T} = T
-
-function (l::CategoricalLikelihood{true})(f::AbstractVector{<:Real})
-    return Categorical(l.invlink(vcat(f, 0)))
-end
-function (l::CategoricalLikelihood{false})(f::AbstractVector{<:Real})
+function (l::CategoricalLikelihood)(f::AbstractVector{<:Real})
     return Categorical(l.invlink(f))
 end
 
-function (l::CategoricalLikelihood{true})(fs::AbstractVector)
-    return Product(Categorical.(l.invlink.(vcat.(fs, 0))))
-end
-function (l::CategoricalLikelihood{false})(fs::AbstractVector)
+function (l::CategoricalLikelihood)(fs::AbstractVector)
     return Product(Categorical.(l.invlink.(fs)))
 end
diff --git a/src/links.jl b/src/links.jl
index d87cdc4..dba07f3 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -27,6 +27,28 @@ end
 
 Base.inv(l::Link) = Link(InverseFunctions.inverse(l.f))
 
+"""
+    SimplexBijectiveLink(link)
+
+Wrapper to preprocess the inputs by adding a `0` at the end before passing it to 
+the link `link`.
+This is a necessary step to work with simplices.
+For example with the [`SoftMaxLink`](@ref), to obtain a `n`-simplex leading to
+`n+1` categories for the [`CategoricalLikelihood`],
+one needs to pass `n+1` latent GP.
+However, by wrapping the link into a `SimplexBijectiveLink`, only `n` latent are needed. 
+"""
+struct SimplexBijectiveLink{L} <: AbstractLink
+    link::L
+end
+
+(l::SimplexBijectiveLink)(f::AbstractVector{<:Real}) = l.link(vcat(f, 0))
+
+make_bijective(l::AbstractLink, ::Val{true}) = SimplexBijectiveLink(l)
+make_bijective(l::AbstractLink, ::Val{false}) = l
+make_bijective(l::AbstractLink, bijective::Bool) = make_bijective(l, Val(bijective))
+
+
 # alias
 const LogLink = Link{typeof(log)}
 const ExpLink = Link{typeof(exp)}
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index b09c103..c3029e7 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,5 +1,5 @@
 @testset "CategoricalLikelihood" begin
-    Catbij = CategoricalLikelihood{true,SoftMaxLink}
+    Catbij = CategoricalLikelihood{SimplexBijectiveLink{SoftMaxLink}}
     for args in ((), (softmax,), (SoftMaxLink(),)),
         kwargs in ((), (; bijective=true), (; bijective=Val(true)))
 
@@ -9,7 +9,7 @@
         end
     end
 
-    Catnonbij = CategoricalLikelihood{false,SoftMaxLink}
+    Catnonbij = CategoricalLikelihood{SoftMaxLink}
     for args in ((), (softmax,), (SoftMaxLink(),)),
         kwargs in ((; bijective=false), (; bijective=Val(false)))
 
diff --git a/test/links.jl b/test/links.jl
index d4e4aa2..f7be88b 100644
--- a/test/links.jl
+++ b/test/links.jl
@@ -7,6 +7,14 @@
     l = Link(f)
     @test l(x) == f(x)
 
+    ## SimplexBijective link
+    l = SoftMaxLink()
+    sbl = SimplexBijectiveLink(l)
+    @test sbl(xs) == l(vcat(xs, 0))
+    @test GPLikelihoods.make_bijective(l, false) isa SoftMaxLink
+    @test GPLikelihoods.make_bijective(l, Val(false)) isa SoftMaxLink
+    @test GPLikelihoods.make_bijective(l, true) isa SimplexBijectiveLink{SoftMaxLink}
+    @test GPLikelihoods.make_bijective(l, Val(true)) isa SimplexBijectiveLink{SoftMaxLink}
     # Log
     l = LogLink()
     @test l(x) == log(x)

From c1ce24e7d031bf50588b2ea82b019c774a164c4c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:01:17 +0100
Subject: [PATCH 40/44] Formatting

---
 src/links.jl  | 1 -
 test/links.jl | 1 +
 2 files changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/links.jl b/src/links.jl
index dba07f3..a02908f 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -48,7 +48,6 @@ make_bijective(l::AbstractLink, ::Val{true}) = SimplexBijectiveLink(l)
 make_bijective(l::AbstractLink, ::Val{false}) = l
 make_bijective(l::AbstractLink, bijective::Bool) = make_bijective(l, Val(bijective))
 
-
 # alias
 const LogLink = Link{typeof(log)}
 const ExpLink = Link{typeof(exp)}
diff --git a/test/links.jl b/test/links.jl
index f7be88b..4d4b578 100644
--- a/test/links.jl
+++ b/test/links.jl
@@ -15,6 +15,7 @@
     @test GPLikelihoods.make_bijective(l, Val(false)) isa SoftMaxLink
     @test GPLikelihoods.make_bijective(l, true) isa SimplexBijectiveLink{SoftMaxLink}
     @test GPLikelihoods.make_bijective(l, Val(true)) isa SimplexBijectiveLink{SoftMaxLink}
+
     # Log
     l = LogLink()
     @test l(x) == log(x)

From 74f6bbb678414ee49dd46540a9768550dc846ae8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:03:49 +0100
Subject: [PATCH 41/44] Update docs

---
 src/likelihoods/categorical.jl | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index f0e717c..9d8d2f0 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -3,18 +3,23 @@
 
 Categorical likelihood is to be used if we assume that the 
 uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) with `n` categories.
-```math
-    p(y|f_1, f_2, \\dots, f_{n-1}) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_{n-1}, 0))
-    p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
-```
+
 Two variants are possible (you can use a `Bool` or `Val{true}`/`Val{false}` but
 we recommend the latter for type stability).
 ## `bijective=true/Val{true}`
+```math
+    p(y|f_1, f_2, \\dots, f_{n-1}) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_{n-1}, 0))
+```
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n-1}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n-1}, 0)``.
+Under the hood, the link `l` is wrapped into a [`SimplexBijectiveLink`](@ref) which takes
+care of concatenating `0`.
 It is used by default.
 
 ## `bijective=false`
+```math
+    p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
+```
 Given an `AbstractVector` ``[f_1, f_2, ..., f_{n}]``, returns a `Categorical` distribution,
 with probabilities given by ``l(f_1, f_2, ..., f_{n})``.
 This variant is over-parametrized, as there are `n-1` independent parameters 

From 777ba74b29fe83c7f84b4ebb4366601297fdeb49 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:42:27 +0100
Subject: [PATCH 42/44] Adressed comments

---
 src/likelihoods/categorical.jl | 31 +++++++++++++------------------
 src/links.jl                   | 14 +++++---------
 2 files changed, 18 insertions(+), 27 deletions(-)

diff --git a/src/likelihoods/categorical.jl b/src/likelihoods/categorical.jl
index 9d8d2f0..10c5c36 100644
--- a/src/likelihoods/categorical.jl
+++ b/src/likelihoods/categorical.jl
@@ -1,27 +1,26 @@
 """
-    CategoricalLikelihood(l=softmax; bijective::Union{Bool,Val{false},Val{true}}=Val(true))
+    CategoricalLikelihood(l=BijectiveSimplexLink(softmax))
 
 Categorical likelihood is to be used if we assume that the 
-uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) with `n` categories.
+uncertainty associated with the data follows a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution).
 
-Two variants are possible (you can use a `Bool` or `Val{true}`/`Val{false}` but
-we recommend the latter for type stability).
-## `bijective=true/Val{true}`
+Assuming a distribution with `n` categories:
+
+## `n-1` inputs (bijective link)
+
+One can work with a bijective transformation by wrapping a link (like `softmax`)
+into a [`BijectiveSimplexLink`](@ref) and only needs `n-1` inputs:
 ```math
     p(y|f_1, f_2, \\dots, f_{n-1}) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_{n-1}, 0))
 ```
-Given an `AbstractVector` ``[f_1, f_2, ..., f_{n-1}]``, returns a `Categorical` distribution,
-with probabilities given by ``l(f_1, f_2, ..., f_{n-1}, 0)``.
-Under the hood, the link `l` is wrapped into a [`SimplexBijectiveLink`](@ref) which takes
-care of concatenating `0`.
-It is used by default.
+The default constructor is a bijective link around `softmax`.
 
-## `bijective=false`
+## `n` inputs (non-bijective link)
+
+One can also pass directly the inputs without concatenating a `0`:
 ```math
     p(y|f_1, f_2, \\dots, f_n) = \\operatorname{Categorical}(y | l(f_1, f_2, \\dots, f_n))
 ```
-Given an `AbstractVector` ``[f_1, f_2, ..., f_{n}]``, returns a `Categorical` distribution,
-with probabilities given by ``l(f_1, f_2, ..., f_{n})``.
 This variant is over-parametrized, as there are `n-1` independent parameters 
 embedded in a `n` dimensional parameter space.
 For more details, see the end of the section of this [Wikipedia link](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions)
@@ -31,11 +30,7 @@ struct CategoricalLikelihood{Tl<:AbstractLink} <: AbstractLikelihood
     invlink::Tl
 end
 
-function CategoricalLikelihood(
-    l=softmax; bijective::Union{Bool,Val{true},Val{false}}=Val(true)
-)
-    return CategoricalLikelihood(make_bijective(link(l), bijective))
-end
+CategoricalLikelihood(l=BijectiveSimplexLink(softmax)) = CategoricalLikelihood(link(l))
 
 function (l::CategoricalLikelihood)(f::AbstractVector{<:Real})
     return Categorical(l.invlink(f))
diff --git a/src/links.jl b/src/links.jl
index ae55089..e7e66c9 100644
--- a/src/links.jl
+++ b/src/links.jl
@@ -31,25 +31,21 @@ link(l::AbstractLink) = l
 Base.inv(l::Link) = Link(InverseFunctions.inverse(l.f))
 
 """
-    SimplexBijectiveLink(link)
+    BijectiveSimplexLink(link)
 
 Wrapper to preprocess the inputs by adding a `0` at the end before passing it to 
 the link `link`.
 This is a necessary step to work with simplices.
 For example with the [`SoftMaxLink`](@ref), to obtain a `n`-simplex leading to
-`n+1` categories for the [`CategoricalLikelihood`],
+`n+1` categories for the [`CategoricalLikelihood`](@ref),
 one needs to pass `n+1` latent GP.
-However, by wrapping the link into a `SimplexBijectiveLink`, only `n` latent are needed. 
+However, by wrapping the link into a `BijectiveSimplexLink`, only `n` latent are needed. 
 """
-struct SimplexBijectiveLink{L} <: AbstractLink
+struct BijectiveSimplexLink{L} <: AbstractLink
     link::L
 end
 
-(l::SimplexBijectiveLink)(f::AbstractVector{<:Real}) = l.link(vcat(f, 0))
-
-make_bijective(l::AbstractLink, ::Val{true}) = SimplexBijectiveLink(l)
-make_bijective(l::AbstractLink, ::Val{false}) = l
-make_bijective(l::AbstractLink, bijective::Bool) = make_bijective(l, Val(bijective))
+(l::BijectiveSimplexLink)(f::AbstractVector{<:Real}) = l.link(vcat(f, 0))
 
 # alias
 const LogLink = Link{typeof(log)}

From c0c7d053b20cf6ec7b725aa06013d74d25aa1778 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:49:55 +0100
Subject: [PATCH 43/44] Corrected changes

---
 src/GPLikelihoods.jl            |  1 +
 test/likelihoods/categorical.jl | 23 ++++-------------------
 test/links.jl                   |  6 +-----
 3 files changed, 6 insertions(+), 24 deletions(-)

diff --git a/src/GPLikelihoods.jl b/src/GPLikelihoods.jl
index 1640577..34890ca 100644
--- a/src/GPLikelihoods.jl
+++ b/src/GPLikelihoods.jl
@@ -16,6 +16,7 @@ export BernoulliLikelihood,
     GammaLikelihood
 export Link,
     ChainLink,
+    BijectiveSimplexLink,
     ExpLink,
     LogLink,
     InvLink,
diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index c3029e7..4db61b8 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,27 +1,12 @@
 @testset "CategoricalLikelihood" begin
-    Catbij = CategoricalLikelihood{SimplexBijectiveLink{SoftMaxLink}}
-    for args in ((), (softmax,), (SoftMaxLink(),)),
-        kwargs in ((), (; bijective=true), (; bijective=Val(true)))
+    @test CategoricalLikelihood() isa CategoricalLikelihood{<:GPLikelihoods.BijectiveSimplexLink}
 
-        @test CategoricalLikelihood(args...; kwargs...) isa Catbij
-        if kwargs != (; bijective=true) # Inferred does not pass with Bool keyword
-            @inferred CategoricalLikelihood(args...; kwargs...)
-        end
-    end
-
-    Catnonbij = CategoricalLikelihood{SoftMaxLink}
-    for args in ((), (softmax,), (SoftMaxLink(),)),
-        kwargs in ((; bijective=false), (; bijective=Val(false)))
-
-        @test CategoricalLikelihood(args...; kwargs...) isa Catnonbij
-        if kwargs != (; bijective=false) # Inferred does not pass with Bool keyword
-            @inferred CategoricalLikelihood(args...; kwargs...)
-        end
-    end
+    @test CategoricalLikelihood(softmax) isa CategoricalLikelihood{SoftMaxLink}
+    @test CategoricalLikelihood(SoftMaxLink()) isa CategoricalLikelihood{SoftMaxLink}
 
     OUT_DIM = 4
     lik_bijective = CategoricalLikelihood()
     test_interface(lik_bijective, Categorical, OUT_DIM)
-    lik_nonbijective = CategoricalLikelihood(softmax; bijective=Val(false))
+    lik_nonbijective = CategoricalLikelihood(softmax)
     test_interface(lik_nonbijective, Categorical, OUT_DIM)
 end
diff --git a/test/links.jl b/test/links.jl
index d6ea21e..67c1af3 100644
--- a/test/links.jl
+++ b/test/links.jl
@@ -12,12 +12,8 @@
 
     ## SimplexBijective link
     l = SoftMaxLink()
-    sbl = SimplexBijectiveLink(l)
+    sbl = BijectiveSimplexLink(l)
     @test sbl(xs) == l(vcat(xs, 0))
-    @test GPLikelihoods.make_bijective(l, false) isa SoftMaxLink
-    @test GPLikelihoods.make_bijective(l, Val(false)) isa SoftMaxLink
-    @test GPLikelihoods.make_bijective(l, true) isa SimplexBijectiveLink{SoftMaxLink}
-    @test GPLikelihoods.make_bijective(l, Val(true)) isa SimplexBijectiveLink{SoftMaxLink}
 
     # Log
     l = LogLink()

From 316d7394e0b6aebc35954339552bf88b7a06d46a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Fri, 28 Jan 2022 16:58:12 +0100
Subject: [PATCH 44/44] Update test/likelihoods/categorical.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 test/likelihoods/categorical.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/test/likelihoods/categorical.jl b/test/likelihoods/categorical.jl
index 4db61b8..8ed48be 100644
--- a/test/likelihoods/categorical.jl
+++ b/test/likelihoods/categorical.jl
@@ -1,5 +1,6 @@
 @testset "CategoricalLikelihood" begin
-    @test CategoricalLikelihood() isa CategoricalLikelihood{<:GPLikelihoods.BijectiveSimplexLink}
+    @test CategoricalLikelihood() isa
+        CategoricalLikelihood{<:GPLikelihoods.BijectiveSimplexLink}
 
     @test CategoricalLikelihood(softmax) isa CategoricalLikelihood{SoftMaxLink}
     @test CategoricalLikelihood(SoftMaxLink()) isa CategoricalLikelihood{SoftMaxLink}