Principal component analysis (PCA) [1] is a famous technique for feature extraction and dimensionality reduction. Despite its widespread use and effectiveness, PCA is constrained by its linear nature.

Probabilistic PCA [2] improves upon classical PCA by linking it with maximum likelihood estimation based on a probability density model of the observed data.

The task of the student is to read about probabilistic PCA. The  student should understand the underlying theoretical concepts of the algorithm, its application spectrum, as well as its limitations.

[1] https://arxiv.org/pdf/1404.1100.pdf

[2] https://www.cs.columbia.edu/~blei/seminar/2020-representation/readings/TippingBishop1999.pdf

Information Theory, Linear Algebra