Statistical Analysis of Distance Estimators with Density Differences and Density Ratios

Entropy

Takafumi Kanamori¹ 

[1] Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan

关键词: density difference;    density ratio;    L₁-distance;    Bregman score;    robustness;   

DOI  :  10.3390/e16020921

来源: mdpi

【 摘 要 】

Estimating a discrepancy between two probability distributions from samples is an important task in statistics and machine learning. There are mainly two classes of discrepancy measures: distance measures based on the density difference, such as the L_p-distances, and divergence measures based on the density ratio, such as the ϕ-divergences. The intersection of these two classes is the L₁-distance measure, and thus, it can be estimated either based on the density difference or the density ratio. In this paper, we first show that the Bregman scores, which are widely employed for the estimation of probability densities in statistical data analysis, allows us to estimate the density difference and the density ratio directly without separately estimating each probability distribution. We then theoretically elucidate the robustness of these estimators and present numerical experiments.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland