Nonparametric estimation of the likelihood ratio and divergence functionals

被引：14
|
作者：
Nguyen, XuanLong [1 ]
Wainwright, Martin J. [1 ]
Jordan, Michael I. [1 ]
机构：
[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA
来源：
2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 | 2007年
关键词：
D O I：
10.1109/ISIT.2007.4557517
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
We develop and analyze a nonparametric method for estimating the class of f-divergence functionals, and the density ratio of two probability distributions. Our method is based on a non-asymptotic variational characterization of the f-divergence, which allows us to cast the problem of estimating divergences in terms of risk minimization. We thus obtain an M-estimator for divergences, based on a convex and differentiable optimization problem that can be solved efficiently We analyze the consistency and convergence rates for this M-estimator given conditions only on the ratio of densities.
引用
收藏
页码：2016 / 2020
页数：5
相关论文
共 50 条
  • [21] Nonparametric inference with generalized likelihood ratio tests
    Mueller, Hans-Georg
    TEST, 2007, 16 (03) : 450 - 452
  • [22] Nonparametric inference with generalized likelihood ratio tests
    Jianqing Fan
    Jiancheng Jiang
    TEST, 2007, 16 : 409 - 444
  • [23] On maximum likelihood estimation and divergence minimization
    Chan, TH
    Yeung, RW
    ISIT: 2002 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2002, : 158 - 158
  • [24] Maximum Likelihood Estimation of Functionals of Discrete Distributions
    Jiao, Jiantao
    Venkat, Kartik
    Han, Yanjun
    Weissman, Tsachy
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (10) : 6774 - 6798
  • [25] ROBUST LIKELIHOOD RATIO TEST USING α- DIVERGENCE
    Rekavandi, Aref Miri
    Seghouane, Abd-Krim
    Evans, Robin J.
    2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, 2020, : 1150 - 1154
  • [26] Nonparametric Estimation of Kullback-Leibler Divergence
    Zhang, Zhiyi
    Grabchak, Michael
    NEURAL COMPUTATION, 2014, 26 (11) : 2570 - 2593
  • [27] Asymptotically efficient nonparametric estimation of nonlinear spectral functionals
    Ginovian, MS
    ACTA APPLICANDAE MATHEMATICAE, 2003, 78 (1-3) : 145 - 154
  • [28] Nonparametric maximum likelihood estimation for shifted curves
    Ronn, BB
    JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2001, 63 : 243 - 259
  • [29] On nonparametric maximum likelihood estimation with double truncation
    Xiao, J.
    Hudgens, M. G.
    BIOMETRIKA, 2019, 106 (04) : 989 - 996
  • [30] Boosting in Univariate Nonparametric Maximum Likelihood Estimation
    Li, YunPeng
    Ye, ZhaoHui
    IEEE SIGNAL PROCESSING LETTERS, 2021, 28 : 623 - 627
12345