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arXiv · 1210.0864

Learning mixtures of structured distributions over discrete domains

Siu-on Chan·Ilias Diakonikolas·Rocco A. Servedio·Xiaorui Sun
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Abstract

Let $\mathfrak{C}$ be a class of probability distributions over the discrete domain $[n] = \{1,...,n\}.$ We show that if $\mathfrak{C}$ satisfies a rather general condition -- essentially, that each distribution in $\mathfrak{C}$ can be well-approximated by a variable-width histogram with few bins -- then there is a highly efficient (both in terms of running time and sample complexity) algorithm that can learn any mixture of $k$ unknown distributions from $\mathfrak{C}.$ We analyze several natural types of distributions over $[n]$, including log-concave, monotone hazard rate and unimodal distributions, and show that they have the required structural property of being well-approximated by a histogram with few bins. Applying our general algorithm, we obtain near-optimally efficient algorithms for all these mixture learning problems.

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Siu-on Chan, Ilias Diakonikolas, Rocco A. Servedio, Xiaorui Sun. 2012-10-02. Learning mixtures of structured distributions over discrete domains. https://arxiv.org/abs/1210.0864

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