Learning Mixtures of Gaussians with Censored Data

2023/05/06 by Tai, Wai Ming, Aragam, Bryon · 1 citation
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2305.04127

Abstract

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 ∑_i=1^k w_i N(μ_i,σ²), 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 μ_i. We propose an algorithm that takes only \frac1ε^O(k) samples to estimate the weights w_i and the means μ_i within ε error.

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