Convex regression with interpretable sharp partitions

Ashley Petersen, Noah Simon, Daniela Witten

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalJournal of Machine Learning Research
StatePublished - Jun 1 2016

Bibliographical note

Funding Information:
We thank the associate editor and three referees for helpful comments. D.W. was supported by NIH Grant DP5OD009145, NSF CAREER Award DMS-1252624, and an Alfred P. Sloan Foundation Research Fellowship. N.S. was supported by NIH Grant DP5OD019820.

Publisher Copyright:
©2016 Ashley Petersen, Noah Simon, and Daniela Witten.


  • Convex optimization
  • Interpretability
  • Non-additivity
  • Non-parametric regression
  • Prediction


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