A Convex Relaxation for Weakly Supervised Classifiers
This work addresses the issue of local minima in weakly supervised classification, which is a problem for researchers and practitioners in machine learning, though it appears incremental as it builds on existing methods with a convex relaxation approach.
The paper tackles the problem of local minima in weakly supervised classification by introducing a convex relaxation of the soft-max loss and an efficient algorithm to solve it, showing favorable empirical performance on datasets for multiple instance learning, semi-supervised learning, and clustering tasks.
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.