On a Scalable Entropic Breaching of the Overfitting Barrier for Small Data Problems in Machine Learning.

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Abstract

Overfitting and treatment of small data are among the most challenging problems in machine learning (ML), when a relatively small data statistics size
T
is not enough to provide a robust ML fit for a relatively large data feature dimension
D
. Deploying a massively parallel ML analysis of generic classification problems for different
D
and
T
, we demonstrate the existence of statistically significant linear overfitting barriers for common ML methods. The results reveal that for a robust classification of bioinformatics-motivated generic problems with the long short-term memory deep learning classifier (LSTM), one needs in the best case a statistics
T
that is at least 13.8 times larger than the feature dimension
D
. We show that this overfitting barrier can be breached at a 10

–
12

fraction of the computational cost by means of the entropy-optimal scalable probabilistic approximations algorithm (eSPA), performing a joint solution of the entropy-optimal Bayesian network inference and feature space segmentation problems. Application of eSPA to experimental single cell RNA sequencing data exhibits a 30-fold classification performance boost when compared to standard bioinformatics tools and a 7-fold boost when compared to the deep learning LSTM classifier.