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Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Affiliation(s)
- Keisuke Yano
- The Institute of Statistical Mathematics, 10-3 Midori cho, Tachikawa City, Tokyo, 190-8562, Japan
| | - Ryoya Kaneko
- Tokyo Marine Holdings, Inc., 1-2-1 Marunouchi, Chiyoda-ku, Tokyo, 100-8050, Japan
| | - Fumiyasu Komaki
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
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Abstract
This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of frequentist risk function. Some applications, such as classification and divergence function estimation, are addressed.
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