Exercise(s) to Classify Genomic Sequences into Coding and Non-Coding

Data

To train, validate and test binary sequence (=time-series) classification methods we use DNA sequences that are either

• completely coding or
• completely non-coding These sequences are data from
  Mertsch and Stanke, End-to-end Learning of Evolutionary Models to Find Coding Regions in Genome Alignments, bioRxiv 2021

Models to Compare

Let $k\in {0,1,2,\dots}$ be a model order. Let $x \in {a,c,g,t}^\ell$ be an input DNA sequence of length $\ell$. Let $y\in{0,1}$ be a class, here $y=1$ means coding (=positive) and $y=0$ (=negative) means non-coding.

1. Two $k$-th order Markov chains, one for coding, one for non-coding, trained individually to maximize the likelihood of the respective data.
2. Like 1., but the positive model is 3-periodic.
3. Two $k$-th order Markov chains, one for coding, one for non-coding. Then logistic regression to predict a probability of coding. Trained (discriminately) to miminize cross-entropy error (CEE).
4. Like 3, but the positive model is 3-periodic.
5. Like 4, but $M>2$ models are allowed and $M$ is optimized.
6. $M$ HMMs with a fixed number of states ($n=3$) are trained jointly with logistic regression.

Compare the Accuracy of above Models on the Test Data