Reviews: Trimmed Density Ratio Estimation

Summary: This paper proposes a "trimmed" estimator that robustly (to outliers) estimates the ratio of two densities, assuming an a exponential family model. This robustness is important, as density ratios can inherently be very unstable when the denominator is small. The proposed model is based on an optimization problem, motivated by minimizing KL divergence between the two densities in the ratio, and is made more computationally tractable by re-expressing it in terms of an equivalent saddle-point/max-min formulation. Similar to the one-class SVM, this formulation explicitly discards a portion (determined by a tuning parameter) of "outlier" samples. The density-ratio estimator is shown to be consistent in two practical settings, one in which the data contains a small portion of explicit outliers and another in which the estimand is intrinsically unstable.