# A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm

arXiv: https://arxiv.org/abs/2012.01929 · HTML: https://mlsanity.com/paper/2012.01929/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Stochastic Approximation Beyond Gradient for Signal Processing and Machine Learning](https://mlsanity.com/paper/2302.11147/) (2023)
- [Stochastic Variable Metric Proximal Gradient with variance reduction for non-convex composite optimization](https://mlsanity.com/paper/2301.00631/) (2023)
- [Towards frugal unsupervised detection of subtle abnormalities in medical imaging](https://mlsanity.com/paper/2309.02458/) (2023)

## Abstract (arXiv)

The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called textttSPIDER-EM, for inference from a training set of size n, n gg 1. At the core of our algorithm is an estimator of the full conditional expectation in the sf E-step, adapted from the stochastic path-integrated differential estimator (tt SPIDER) technique. We derive finite-time complexity bounds for smooth non-convex likelihood: we show that for convergence to an ε-approximate stationary point, the complexity scales as K_operatornameOpt (n,ε )=cal O(ε-1) and K_operatornameCE( n,ε ) = n+ √n cal O(ε-1 ), where K_operatornameOpt( n,ε ) and K_operatornameCE(n, ε ) are respectively the number of sf M-steps and the number of per-sample conditional expectations evaluations. This improves over the state-of-the-art algorithms. Numerical results support our findings.