On a scalable entropic breaching of the overfitting barrier in machine learning
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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.
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