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Multivariate convex regression with adaptive partitioning

Publication ,  Journal Article
Hannah, LA; Dunson, DB
Published in: Journal of Machine Learning Research
November 1, 2013

We propose a new, nonparametric method for multivariate regression subject to convexity or concavity constraints on the response function. Convexity constraints are common in economics, statistics, operations research, financial engineering and optimization, but there is currently no multivariate method that is stable and computationally feasible for more than a few thousand observations. We introduce convex adaptive partitioning (CAP), which creates a globally convex regression model from locally linear estimates fit on adaptively selected covariate partitions. CAP is a computationally efficient, consistent method for convex regression. We demonstrate empirical performance by comparing the performance of CAP to other shape-constrained and unconstrained regression methods for predicting weekly wages and value function approximation for pricing American basket options. © 2013 Lauren A. Hannah and David B. Dunson.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

November 1, 2013

Volume

14

Start / End Page

3153 / 3188

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

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ICMJE
MLA
NLM
Hannah, L. A., & Dunson, D. B. (2013). Multivariate convex regression with adaptive partitioning. Journal of Machine Learning Research, 14, 3153–3188.
Hannah, L. A., and D. B. Dunson. “Multivariate convex regression with adaptive partitioning.” Journal of Machine Learning Research 14 (November 1, 2013): 3153–88.
Hannah LA, Dunson DB. Multivariate convex regression with adaptive partitioning. Journal of Machine Learning Research. 2013 Nov 1;14:3153–88.
Hannah, L. A., and D. B. Dunson. “Multivariate convex regression with adaptive partitioning.” Journal of Machine Learning Research, vol. 14, Nov. 2013, pp. 3153–88.
Hannah LA, Dunson DB. Multivariate convex regression with adaptive partitioning. Journal of Machine Learning Research. 2013 Nov 1;14:3153–3188.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

November 1, 2013

Volume

14

Start / End Page

3153 / 3188

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences