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CORR
2008
Springer

Estimating divergence functionals and the likelihood ratio by convex risk minimization

13 years 3 months ago
Estimating divergence functionals and the likelihood ratio by convex risk minimization
We develop and analyze M-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of f-divergences, which allows the problem of estimating divergences to be tackled via convex empirical risk optimization. The resulting estimators are simple to implement, requiring only the solution of standard convex programs. We present an analysis of consistency and convergence for these estimators. Given conditions only on the ratios of densities, we show that our estimators can achieve optimal minimax rates for the likelihood ratio in certain regimes. We derive an efficient optimization algorithm for computing our estimates, and illustrate their convergence behavior and practical viability by simulations.1
XuanLong Nguyen, Martin J. Wainwright, Michael I.
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors XuanLong Nguyen, Martin J. Wainwright, Michael I. Jordan
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