Sparse High-Dimensional Isotonic Regression

07/03/2019 ∙ by David Gamarnik, et al. ∙ 0

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 standard methods.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.