Abstract
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geometric rate and attains an estimator with the (near-)optimal statistical rate of convergence. (ii) Based on the obtained estimator, we propose a new inferential procedure for testing hypotheses for low dimensional components of high dimensional parameters. For a broad family of statistical models, our framework establishes the first computationally feasible approach for optimal estimation and asymptotic inference in high dimensions.
Original language | English (US) |
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Pages (from-to) | 2521-2529 |
Number of pages | 9 |
Journal | Advances in Neural Information Processing Systems |
Volume | 2015-January |
State | Published - 2015 |
Event | 29th Annual Conference on Neural Information Processing Systems, NIPS 2015 - Montreal, Canada Duration: Dec 7 2015 → Dec 12 2015 |
All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Information Systems
- Signal Processing