# Nonparametric Reduced Rank Regression

arXiv: https://arxiv.org/abs/1301.1919 · HTML: https://mlsanity.com/paper/1301.1919/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2013.

## Built on by (most cited first, 1 of 1)

- [Vector-Valued Least-Squares Regression under Output Regularity Assumptions](https://mlsanity.com/paper/2211.08958/) (2022)

## Abstract (arXiv)

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.