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TITLE: Multivariate Convex Regression for Value Function Approximation
SPEAKER: Lauren Hannah
ABSTRACT:
We propose two 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 computationally feasible for more than a few hundred observations. We introduce Convex Adaptive Partitioning (CAP) and Multivariate Bayesian Convex Regression (MBCR), which create a globally convex regression model from locally linear estimates fit on adaptively selected covariate partitions. CAP is computationally efficient, with O(n log(n) log(log(n))) computational complexity, as well as statistically consistent. Although inference for MBCR is more difficult than that of CAP, we show that MBCR is not only consistent but has minimax-optimal adaptive convergence rates. These methods are tested on value function approximation settings in exotic options pricing and response surface methods for simulation optimization.
