Partial Least Squares (PLS) — how is it different from PCR?

hard

Answer

$PCR: PCA components chosen by max variance in X (Y-ignorant).$
$PLS: components maximize covariance with Y (supervised DR).$
$Better prediction for high-dim, multicollinear data (spectroscopy, genomics, chemometrics).$
$Fit iteratively: extract latent variable, deflate X and Y, repeat.$
$Bridge between PCA and OLS.$
$Standard in chemometrics, increasingly used in bioinformatics.$

Check yourself — multiple choice

Same as PCR
Components maximize cov(X, Y) supervised (vs PCR's variance-only, Y-ignorant); better prediction in high-dim multicollinear data (spectroscopy, genomics)
Random
Not real

PLS: supervised DR maximizing cov(X, Y); better than PCR for prediction.

#dimensionality-reduction#regression

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