# EM algorithm for PCA

(35 minutes to learn)

## Summary

While probabilistic PCA has a closed-form solution, it is infeasible to compute for large and high-dimensional datasets. The expectation-maximization (EM) algorithm provides an alternative. Despite its iterative nature, it can be far more computationally efficient.

## Context

This concept has the prerequisites:

- Expectation-Maximization algorithm
- probabilistic PCA (EM is a way of fitting the probabilistic PCA model.)
- maximum likelihood: multivariate Gaussians (The M step involves maximum likelihood for multivariate Gaussians.)

## Core resources (read/watch one of the following)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 12.2.5, pages 396-398

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 12.2.2, pages 577-580

## See also

-No Additional Notes-