Precise Performance Analysis of Extended Margin Maximizers (EMM) on Separable Data

Jul 12, 2020

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Logistic models are commonly used for binary classification tasks. The success of such models has often been attributed to their connection to maximum-likelihood estimators. It has been shown that SGD algorithms , when applied on the logistic loss, converge to the max-margin classifier (a.k.a. hard-margin SVM). The performance of hard-margin SVM has been recently analyzed in <cit.>. Inspired by these results, in this paper, we present and study a more general setting, where the underlying parameters of the logistic model possess certain structures (sparse, block-sparse, low-rank, etc.) and introduce a more general framework (which is referred to as “Generalized Margin Maximizer”, GMM). While classical max-margin classifiers minimize the 2-norm of the parameter vector subject to linearly separating the data, GMM minimizes any arbitrary convex function of the parameter vector. We provide a precise performance analysis of the generalization error of such methods and show improvement over the max-margin method which does not take into account the structure of the model. In future work we show that mirror descent algorithms, with a properly tuned step size, can be exploited to achieve GMM classifiers. Our theoretical results are validated by extensive simulation results across a range of parameter values, problem instances, and model structures.

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About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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