A unified implicit moment tensor estimation framework yields poly(d,k)-time learners for mixtures of linear regressions, spherical Gaussians, and positive sums of ReLU activations, with one unproven step in the regression application.
Robust Learning of Mixtures of Gaussians
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abstract
We resolve one of the major outstanding problems in robust statistics. In particular, if $X$ is an evenly weighted mixture of two arbitrary $d$-dimensional Gaussians, we devise a polynomial time algorithm that given access to samples from $X$ an $\eps$-fraction of which have been adversarially corrupted, learns $X$ to error $\poly(\eps)$ in total variation distance.
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2024 1verdicts
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Implicit High-Order Moment Tensor Estimation and Learning Latent Variable Models
A unified implicit moment tensor estimation framework yields poly(d,k)-time learners for mixtures of linear regressions, spherical Gaussians, and positive sums of ReLU activations, with one unproven step in the regression application.