Risk bounds for mixture density estimation

DOI10.1051/ps:2005011zbMath1141.62024OpenAlexW2158733996WikidataQ56906344 ScholiaQ56906344MaRDI QIDQ3373741

Alexander Rakhlin, Dmitriy Panchenko, Sayan Mukherjee

Publication date: 9 March 2006

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PS_2005__9__220_0

zbMATH Keywords

maximum likelihoodRademacher processesMixture density estimation

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items (14)

Greedy algorithms for prediction ⋮ Consistency and generalization bounds for maximum entropy density estimation ⋮ Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models ⋮ Density estimation with stagewise optimization of the empirical risk ⋮ The optimal solution of multi-kernel regularization learning ⋮ On approximations via convolution-defined mixture models ⋮ Multi-kernel regularized classifiers ⋮ SIEVE ESTIMATION OF THE MINIMAL ENTROPY MARTINGALE MARGINAL DENSITY WITH APPLICATION TO PRICING KERNEL ESTIMATION ⋮ Approximation by finite mixtures of continuous density functions that vanish at infinity ⋮ Analysis of error propagation in particle filters with approximation ⋮ Optimal Kullback-Leibler aggregation in mixture density estimation by maximum likelihood ⋮ Unregularized online algorithms with varying Gaussians ⋮ Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors ⋮ A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
• Generalization bounds for function approximation from scattered noisy data
• Approximation and estimation bounds for artificial neural networks
• Rates of convergence for minimum contrast estimators
• Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
• Weak convergence and empirical processes. With applications to statistics
• 10.1162/153244302760185225
• Uniform Central Limit Theorems
• Universal approximation bounds for superpositions of a sigmoidal function
• Rates of convergence for the maximum likelihood estimator in mixture models

This page was built for publication: Risk bounds for mixture density estimation