Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective
This work addresses robust scatter estimation for statistics, offering a novel framework that integrates GANs and proper scoring rules, though it is incremental in building on prior connections between robust estimation and GANs.
The paper tackles robust scatter estimation by introducing a learning via classification framework based on proper scoring rules, which connects matrix depth functions and GANs through variational approximations of f-divergences; it proposes new robust scatter estimators with neural network discriminators that achieve minimax rates under Huber's contamination model and demonstrate good performance in numerical experiments.
Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we introduce a general learning via classification framework based on the notion of proper scoring rules. This framework allows us to understand both matrix depth function and various GANs through the lens of variational approximations of $f$-divergences induced by proper scoring rules. We then propose a new class of robust scatter estimators in this framework by carefully constructing discriminators with appropriate neural network structures. These estimators are proved to achieve the minimax rate of scatter estimation under Huber's contamination model. Our numerical results demonstrate its good performance under various settings against competitors in the literature.