Sparse high-dimensional isotonic regression

Gamarnik, David; Gaudio, Julia

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Sparse high-dimensional isotonic regression

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Author(s)

Gamarnik, David

•

Gaudio, Julia

Date Issued

2019

Journal

Advances in Neural Information Processing Systems

Citation

Gamarnik, David and Gaudio, Julia. 2019. "Sparse high-dimensional isotonic regression." Advances in Neural Information Processing Systems, 32.

Version

Final published version

Abstract

© 2019 Neural information processing systems foundation. All rights reserved. We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse isotonic regression setting, which we consider here. We provide an upper bound on the expected VC entropy of the space of sparse coordinate-wise monotone functions, and identify the regime of statistical consistency of our estimator. We also propose a linear program to recover the active coordinates, and provide theoretical recovery guarantees. We close with experiments on cancer classification, and show that our method significantly outperforms several standard methods.

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https://hdl.handle.net/1721.1/137482

DOI of Published Version

https://papers.nips.cc/paper/2019/hash/4fd5aadb85a00525415e3733cb96ed68-Abstract.html