Learning Mixtures of Gaussians with Censored Data

05/06/2023

∙

by   Wai Ming Tai, et al.

∙

0

∙

share

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,σ^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 μ_i. We propose an algorithm that takes only 1/ε^O(k) samples to estimate the weights w_i and the means μ_i within ε error.