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Robust high dimensional expectation maximization algorithm via trimmed hard thresholding
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DOI：10.1007/s10994-020-05926-z.png)
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摘要
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In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space (i.e., d >> n) where the underlying parameter is assumed to be sparse. Specifically, we propose a method called Trimmed (Gradient) Expectation Maximization which adds a trimming gradients step and a hard thresholding step to the Expectation step (E-step) and the Maximization step (M-step), respectively. We show that under some mild assumptions and with an appropriate initialization, the algorithm is corruption-proofing and converges to the (near) optimal statistical rate geometrically when the fraction of the corrupted samples epsilon is bounded by O(1/root n). Moreover, we apply our general framework to three canonical models: mixture of Gaussians, mixture of regressions and linear regression with missing covariates. Our theory is supported by thorough numerical results.
Keyword:
Robust statistics
High dimensional statistics
Gaussian mixture model
Expectation maximixation
Iterative hard thresholding
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