An Efficient and Provable Approach for Mixture Proportion Estimation Using Linear Independence Assumption

Xiyu Yu, Tongliang Liu, Mingming Gong, Kayhan Batmanghelich, Dacheng Tao; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018, pp. 4480-4489

In this paper, we study the mixture proportion estimation (MPE) problem in a new setting: given samples from the mixture and the component distributions, we identify the proportions of the components in the mixture distribution. To address this problem, we make use of a linear independence assumption, i.e., the component distributions are independent from each other, which is much weaker than assumptions exploited in the previous MPE methods. Based on this assumption, we propose a method (1) that uniquely identifies the mixture proportions, (2) whose output provably converges to the optimal solution, and (3) that is computationally efficient. We show the superiority of the proposed method over the state-of-the-art methods in two applications including learning with label noise and semi-supervised learning on both synthetic and real-world datasets.