Principal Component Analysis (PCA) is frequently applied in machine learning as a sort of black box dimensionality reduction technique. PCA can be arrived at as an expression of a best fit probability distribution for our data. Treating PCA as a probability distribution opens up all sorts of fruitful avenues, we can draw new examples from the learned distribution and/or evaluate the likelihood of samples as we observe them to detect outliers.

Asymptotic Labs (Posts about generative models)

PCA and probabilities