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Poster
Beyond black box densities: Parameter learning for the deviated components
Dat Do · Nhat Ho · XuanLong Nguyen

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #819
in Poster Session 3 »
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} $(1-\lambda^{*})h_0 + \lambda^{*} (\sum_{i = 1}^{k} p_{i}^{*} f(x|\theta_{i}^{*}))$, where $h_0$ is a known density function, while the deviated proportion $\lambda^{*}$ and latent mixing measure $G_{*} = \sum_{i = 1}^{k} p_{i}^{*} \delta_{\theta_i^{*}}$ associated with the mixture distribution are unknown. Via a novel notion of distinguishability between the known density $h_{0}$ and the deviated mixture distribution, we establish rates of convergence for the maximum likelihood estimates of $\lambda^{*}$ and $G^{*}$ under Wasserstein metric. Simulation studies are carried out to illustrate the theory.
Keywords: Statistical Learning Theory · Wasserstein Metric · Mixture Model

Author Information

Dat Do (University of Michigan)
Nhat Ho (University of Texas at Austin)
XuanLong Nguyen (University of Michigan)

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