# High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality

arXiv: https://arxiv.org/abs/1412.8729 · HTML: https://mlsanity.com/paper/1412.8729/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2014.

## Built on by (most cited first, 6 of 6)

- [Prediction Sets for High-Dimensional Mixture of Experts Models](https://mlsanity.com/paper/2210.16710/) (2022)
- [The EM Algorithm is Adaptively-Optimal for Unbalanced Symmetric Gaussian Mixtures](https://mlsanity.com/paper/2103.15653/) (2021)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Beyond EM Algorithm on Over-specified Two-Component Location-Scale Gaussian Mixtures](https://mlsanity.com/paper/2205.11078/) (2022)
- [Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequality](https://mlsanity.com/paper/2407.17949/) (2024)
- [Inferring Diffusion Structures of Heterogeneous Network Cascade](https://mlsanity.com/paper/2506.19142/) (2025)

## Abstract (arXiv)

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 new inferential procedures for testing hypotheses and constructing confidence intervals 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. Our theory is supported by thorough numerical results.