Outlier-robust parameter estimation for unnormalized statistical models

Unnormalized statistical models are ubiquitous in modern statistical data analysis. Recent methods take a classification approach to estimate unnormalized models. However, the classification problem is often solved based on the maximum-likelihood estimation, which can be seriously hampered by the contamination of outliers. In this paper, we propose two outlier-robust methods for estimation of unnormalized statistical models. The proposed methods are developed by combining robust divergences with the classification approach, and their robustness is theoretically investigated based on influence function. Interestingly, our theoretical analysis reveals a counter-intuitive robustness of the proposed methods, and shows the importance of not only employing robust divergences but also taking the classification approach for outlier-robust estimation. Finally, we experimentally demonstrate that the proposed methods are robust against outliers.