// ◇ Classical Machine Learning

Expectation–Maximization (EM)

Alternates inferring hidden variables and updating parameters.

期望最大化（EM） 1977 Intermediate extended

IN PLAIN WORDS

The E-step estimates posterior over hidden variables; the M-step re-fits parameters; likelihood never decreases. It trains GMMs and HMMs and inspires VAEs.

Used in: Gaussian mixtures, speech HMMs, missing data

TIMELINE · prerequisites → this → what builds on it

1977 Expectation–Maxim…1982 k-Means Clust…2013 Variational A…

01Original paper

Maximum Likelihood from Incomplete Data Via the EM Algorithm

Dempster et al. · Journal of the Royal Statistical Society Series B: Statistical Methodology · 1977

DOI ↗ ✓ Verified · Crossref API doi:10.1111/j.2517-6161.1977.tb01600.x

02Where it sits

Learn the left column first; the right column builds on this one.

Learn first

k-Means Clustering

Expectation–Maximization (EM)

Then you can learn

Variational Autoencoder (VAE)

Left: prerequisites · right: builds on this · dashed: related. Full map →

03Learning resources

Official docs, explainers, courses and reference code. All links checked.

Official docs

scikit-learn.org ↗EN

Books

04Where the course teaches it

U13 Probability, Statistics & Information Theory Distributions, expectation, Bayes, maximum likelihood, cross-entropy and KL divergence. 12 h3 algorithms0 papers U23 Unsupervised Learning k-means, Gaussian mixtures and EM, PCA, t-SNE/UMAP. 8 h6 algorithms2 papers

For AI / data

Verification: verified, checked 2026-10-21.
JSON: /api/learn/algorithms.json (id: em)