caa a22 4500 605478422 CHVBK 20210128100405.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10994-014-5467-7 doi (NATIONALLICENCE)springer-10.1007/s10994-014-5467-7 Entropic risk minimization for nonparametric estimation of mixing distributions [Elektronische Daten] [Kazuho Watanabe, Shiro Ikeda] We discuss a nonparametric estimation method for the mixing distributions in mixture models. The problem is formalized as a minimization of a one-parameter objective functional, which becomes the maximum likelihood estimation or the kernel vector quantization in special cases. Generalizing the theorem for the nonparametric maximum likelihood estimation, we prove the existence and discreteness of the optimal mixing distribution and provide an algorithm to calculate it. It is demonstrated that with an appropriate choice of the parameter, the proposed method is less prone to overfitting than the maximum likelihood method. We further discuss the connection between the unifying estimation framework and the rate-distortion problem. The Author(s), 2014 Mixture models nationallicence Nonparametric estimation nationallicence Entropic risk measure nationallicence Rate-distortion theory nationallicence Watanabe Kazuho Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1, Hibarigaoka, Tempaku-cho, 441-8580, Toyohashi, Japan aut Ikeda Shiro The Institute of Statistical Mathematics, 10-3, Midori-cho, 190-8562, Tachikawa-shi, Tokyo, Japan aut Machine Learning Springer US; http://www.springer-ny.com 99/1(2015-04-01), 119-136 0885-6125 99:1<119 2015 99 10994 https://doi.org/10.1007/s10994-014-5467-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-014-5467-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Watanabe Kazuho Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1, Hibarigaoka, Tempaku-cho, 441-8580, Toyohashi, Japan aut NATIONALLICENCE 700 1- Ikeda Shiro The Institute of Statistical Mathematics, 10-3, Midori-cho, 190-8562, Tachikawa-shi, Tokyo, Japan aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 99/1(2015-04-01), 119-136 0885-6125 99:1<119 2015 99 10994