Robust Density Ratio Estimation: Trimming the Likelihood Ratio

Density ratio estimation has become a versatile tool in machine learning community recently. However, due to its unbounded nature, density ratio estimation is vulnerable to corrupted data points, which misleads the estimated ratio toward infinity. In this paper, we present a robust estimator which automatically identifies and trims outliers according to the log likelihood ratio values. Such an estimator has a convex formulation and can be efficiently solved. We analyze the \ell_{2} parameter estimation error of such an estimator under two scenarios motivated by real-world problems. Numerical analysis was conducted to verify the effectiveness of such an estimator.