Optimizing Shallow Networks for Binary Classification

TL;DR

This paper introduces a new family of optimization problems for neural network binary classification that differ from existing methods, enabling simpler, stable algorithms potentially more effective than current popular techniques.

Contribution

It presents a novel class of optimization problems for neural networks that are not covered by existing approaches, opening new avenues for training algorithms.

Findings

New optimization algorithms are simple to implement

Algorithms exhibit stable convergence

Potentially outperform existing techniques

Abstract

Data driven classification that relies on neural networks is based on optimization criteria that involve some form of distance between the output of the network and the desired label. Using the same mathematical analysis, for a multitude of such measures, we can show that their optimum solution matches the ideal likelihood ratio test classifier. In this work we introduce a different family of optimization problems which is not covered by the existing approaches and, therefore, opens possibilities for new training algorithms for neural network based classification. We give examples that lead to algorithms that are simple in implementation, exhibit stable convergence characteristics and are antagonistic to the most popular existing techniques.