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Poster

Beyond black box densities: Parameter learning for the deviated components

Dat Do · Nhat Ho · XuanLong Nguyen

Hall J (level 1) #819

Keywords: [ Mixture Model ] [ Statistical Learning Theory ] [ Wasserstein Metric ]


Abstract: As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution. To model this phenomenon, we consider the \emph{deviating mixture model} (1λ)h0+λ(ki=1pif(x|θi)), where h0 is a known density function, while the deviated proportion λ and latent mixing measure G=ki=1piδθi associated with the mixture distribution are unknown. Via a novel notion of distinguishability between the known density h0 and the deviated mixture distribution, we establish rates of convergence for the maximum likelihood estimates of λ and G under Wasserstein metric. Simulation studies are carried out to illustrate the theory.

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