Learning Mixtures of Gaussians with Censored Data

by   Wai Ming Tai, et al.

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians βˆ‘_i=1^k w_i 𝒩(ΞΌ_i,Οƒ^2), i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights w_i and the means ΞΌ_i. We propose an algorithm that takes only 1/Ξ΅^O(k) samples to estimate the weights w_i and the means ΞΌ_i within Ξ΅ error.


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