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.

For many structured learning tasks, the data annotation process is complex and costly. Existing annotation schemes usually aim at acquiring completely annotated structures, under the common perception that partial structures are of low quality and could hurt the learning process. This paper questions this common perception, motivated by the fact that structures consist of interdependent sets of variables. Thus, given a fixed budget, partly annotating each structure may provide the same level of supervision, while allowing for more structures to be annotated. We provide an information theoretic formulation for this perspective and use it, in the context of three diverse structured learning tasks, to show that learning from partial structures can sometimes outperform learning from complete ones. Our findings may provide important insights into structured data annotation schemes and could support progress in learning protocols for structured tasks.