Multivariate convex regression with adaptive partitioning
By Lauren Hannah, David B. Dunson. 2011
137 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Yining Chen
- Richard J. Samworth
- Csaba Szepesvari
- András György
- Gábor Balázs
- Junming Yin
- Yaoliang Yu
- Amir-massoud Farahmand
In Statistics and Probability
- Yining Chen
- Richard J. Samworth
- András György
- Gábor Balázs
- Junming Yin
- Yaoliang Yu
- Csaba Szepesvari
- Nan Jiang
Citations in the corpus
- Convex-constrained Sparse Additive Modeling and Its Extensions (2017, background): “For instance, many functions that arise in econometrics [Var82, Var84], actuarial science [Gre56], statistics [GJ14], and optimization [HD13, HPD14] tend to be convex/concave or monotonic [BBBB72].”
- Near-optimal max-affine estimators for convex regression (2015, methodology): “Furthermore , we included two state of the art max-affine estimators, the convex adaptive partitioning (CAP, Hannah and Dunson 2013) and the least-squares partition algorithm 6 (LSPA, Magnani and Boyd 2009).”
- Generalized additive and index models with shape constraints (2014, methodology): “, 1984), convex adaptive partitioning, CAP (Hannah and Dunson, 2013) and multivariate convex regression, MCR (Lim and Glynn, 2012; Seijo and Sen, 2011).”