  Overfitting and treatment of "small data" are among the most challenging
problems in the 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 $T$, existence of
statistically-significant linear overfitting barriers for common ML methods is
demonstrated. For example, these 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 a best case a
statistics $T$ that is at least 13.8 times larger then the feature dimension
$D$. It is shown 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.
