The interactive film is in the book's Companion

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The Marchenko-Pastur Law and the Escaping Eigenvalue

Chapter 8 · Mathematics for AI and Machine Learning · Advanced · 1:32

An interactive live film: sample covariance eigenvalues of pure noise spread over the Marchenko-Pastur bulk; plant a signal and find the threshold theta = sqrt(gamma) where its eigenvalue escapes.

Narration

Take n samples of p independent noise features, each with variance one, so the true covariance is the identity. Every eigenvalue of the sample covariance should then be close to one.

It is not. The blue bars are the sample eigenvalues for a ratio gamma of one quarter: they spread from one quarter to two and one quarter. The purple curve is the Marchenko Pastur law, which predicts this bulk.

The rest of the narration is in the book's Companion.

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