Interior path following primal-dual algorithms. Part II: Convex quadratic programming
Mathematical Programming: Series A and B
C4.5: programs for machine learning
C4.5: programs for machine learning
Machine Learning
Randomizing Outputs to Increase Prediction Accuracy
Machine Learning
SECRET: a scalable linear regression tree algorithm
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Convex Optimization
Pricing American Options: A Duality Approach
Operations Research
Incremental Learning of Linear Model Trees
Machine Learning
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics)
Approximating optimization problems over convex functions
Numerische Mathematik
On Convex Functions and the Finite Element Method
SIAM Journal on Numerical Analysis
Data Envelopment Analysis as Nonparametric Least-Squares Regression
Operations Research
Nonparametric combinatorial regression for shape constrained modeling
IEEE Transactions on Signal Processing
Multivariate convex support vector regression with semidefinite programming
Knowledge-Based Systems
Hinging hyperplanes for regression, classification, and function approximation
IEEE Transactions on Information Theory
Numerically Convex Forms and Their Application in Gate Sizing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An algorithm for approximating piecewise linear concave functions from sample gradients
Operations Research Letters
Regression methods for pricing complex American-style options
IEEE Transactions on Neural Networks
Consistency of Multidimensional Convex Regression
Operations Research
Response surface computation via simulation in the presence of convexity
Proceedings of the Winter Simulation Conference
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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.