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Nonparametric Reduced Rank Regression
Rina Foygel · Michael Horrell · Mathias Drton · John Lafferty

Thu Dec 06 02:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor #None
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that have low rank. Backfitting algorithms are derived and justified using a nonparametric form of the nuclear norm subdifferential. Oracle inequalities on excess risk are derived that exhibit the scaling behavior of the procedure in the high dimensional setting. The methods are illustrated on gene expression data.

Author Information

Rina Foygel (Stanford University)
Michael Horrell (University of Chicago)
Mathias Drton (University of Washington)
John Lafferty (Yale University)

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