# Geometry of EM and related iterative algorithms

arXiv: https://arxiv.org/abs/2209.01301 · HTML: https://mlsanity.com/paper/2209.01301/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 86 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 11 of 11)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regression](https://mlsanity.com/paper/2006.02601/) (2020)
- [f-GANs in an Information Geometric Nutshell](https://mlsanity.com/paper/1707.04385/) (2017)
- [Modal Principal Component Analysis](https://mlsanity.com/paper/2008.03400/) (2020)
- [Estimation of neural connections from partially observed neural spikes](https://mlsanity.com/paper/1711.03303/) (2017)
- [On a convergence property of a geometrical algorithm for statistical manifolds](https://mlsanity.com/paper/1909.12644/) (2019)
- [Principal component analysis for Gaussian process posteriors](https://mlsanity.com/paper/2107.07115/) (2021)

## Built on by (most cited first, 2 of 2)

- [Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry](https://mlsanity.com/paper/2505.16251/) (2025)
- [Density Operator Expectation Maximization](https://mlsanity.com/paper/2507.22786/) (2025)

## Abstract (arXiv)

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of observables and unobservables. Its general properties are well studied, and also, there are countless ways to apply it to individual problems. In this paper, we introduce the em algorithm, an information geometric formulation of the EM algorithm, and its extensions and applications to various problems. Specifically, we will see that it is possible to formulate an outlier-robust inference algorithm, an algorithm for calculating channel capacity, parameter estimation methods on probability simplex, particular multivariate analysis methods such as principal component analysis in a space of probability models and modal regression, matrix factorization, and learning generative models, which have recently attracted attention in deep learning, from the geometric perspective.