Sparse high-dimensional isotonic regression

© 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 mot...

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Bibliographic Details
Main Authors: Gamarnik, David (Author), Gaudio, Julia (Author)
Other Authors: Sloan School of Management (Contributor), Massachusetts Institute of Technology. Operations Research Center (Contributor)
Format: Article
Language:English
Published: 2021-12-20T19:06:20Z.
Subjects:
Online Access:Get fulltext
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100 1 0 |a Gamarnik, David  |e author 
100 1 0 |a Sloan School of Management  |e contributor 
100 1 0 |a Massachusetts Institute of Technology. Operations Research Center  |e contributor 
700 1 0 |a Gaudio, Julia  |e author 
245 0 0 |a Sparse high-dimensional isotonic regression 
260 |c 2021-12-20T19:06:20Z. 
856 |z Get fulltext  |u https://hdl.handle.net/1721.1/137482.2 
520 |a © 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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655 7 |a Article 
773 |t Advances in Neural Information Processing Systems