A Convex Relaxation for Weakly Supervised Classifiers

TL;DR

This paper presents a convex relaxation approach for weakly supervised classification that improves optimization stability and performance, using a semidefinite programming algorithm, and demonstrates favorable empirical results across various tasks.

Contribution

It introduces a convex relaxation of the soft-max loss for weakly supervised classifiers and an efficient SDP-based algorithm to optimize it, reducing local minima issues.

Findings

Outperforms standard methods on multiple datasets

Effective for multiple instance and semi-supervised learning

Improves clustering performance

Abstract

This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as expectation-maximization (EM), which may lead to local minima. To avoid this problem, we propose a cost function based on a convex relaxation of the soft-max loss. We then propose an algorithm specifically designed to efficiently solve the corresponding semidefinite program (SDP). Empirically, our method compares favorably to standard ones on different datasets for multiple instance learning and semi-supervised learning as well as on clustering tasks.