Sparse high-dimensional isotonic regression
Name
NeurIPS-2019-sparse-high-dimensional-isotonic-regression-Paper.pdf
Description
Published version
Size
309.36 KB
Format
Unknown
Checksum (MD5)
ca4ce87200a56367bd39778e6d5a3ae7
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.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/2019/hash/4fd5aadb85a00525415e3733cb96ed68-Abstract.html
