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Activity Number:
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448
- The Contribution of Convex Optimization to New Statistical Concepts
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Type:
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Topic Contributed
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Date/Time:
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Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
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Sponsor:
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Section on Statistical Computing
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Abstract #312578
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Title:
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A Computational Framework for Multivariate Convex Regression
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Author(s):
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Rahul Mazumder*
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Companies:
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Massachusetts Institute of Technology
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Keywords:
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convex optimization; nonparametric regression; shape constrained regression
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Abstract:
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We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with O(n^2) linear constraints (n being the sample size), is difficult to compute for large problems. Exploiting problem specific structure, we propose a scalable algorithmic framework based on the augmented Lagrangian method to compute the LSE. We develop a novel approach to obtain smooth convex approximations to the fitted (piecewise affine) convex LSE and provide formal bounds on the quality of approximation.
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Authors who are presenting talks have a * after their name.
