Weakly supervised learning via statistical sufficiency

Abstract

The Thesis introduces a novel algorithmic framework for weakly supervised learn- ing, namely, for any any problem in between supervised and unsupervised learning, from the labels standpoint. Weak supervision is the reality in many applications of machine learning where training is performed with partially missing, aggregated- level and/or noisy labels. The approach is grounded on the concept of statistical suf- ficiency and its transposition to loss functions. Our solution is problem-agnostic yet constructive as it boils down to a simple two-steps procedure. First, estimate a suffi- cient statistic for the labels from weak supervision. Second, plug the estimate into a (newly defined) linear-odd loss function and learn the model by any gradient-based solver, with a simple adaptation. We apply the same approach to several challeng- ing learning problems: (i) learning from label proportions, (ii) learning with noisy labels for both linear classifiers and deep neural networks, and (iii) learning from feature-wise distributed datasets where the entity matching function is unknown.