Learning Mixtures of Gaussians with Censored Data

05/06/2023
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by   Wai Ming Tai, et al.
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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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