Name
Title | ||
|---|---|---|
Robust High Dimensional Expectation Maximization Algorithm Via Trimmed Hard Thresholding |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s10994-020-05926-z | MACHINE LEARNING |
Keywords | DocType | Volume |
Robust statistics, High dimensional statistics, Gaussian mixture model, Expectation maximixation, Iterative hard thresholding | Journal | 109 |
Issue | ISSN | Citations |
12 | 0885-6125 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wang, Di | 1 | 8 | 10.59 |
| XiangYu Guo | 2 | 2 | 5.71 |
| Shi Li | 3 | 208 | 22.01 |
| Jinhui Xu | 4 | 665 | 78.86 |