On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models

Abstract

We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models and Delta's method (estimating functions of linear regression models) as well. The algorithms are based on a continuous relaxation of an otherwise intractable combinatorial optimization problem, with sampling or greedy procedures as post-processing steps. Formal approximation guarantees are established for both algorithms, and numerical results on both synthetic and real-world data confirm the effectiveness of the proposed methods.

41 pages. Accepted for publication in Journal of Machine Learning Research

Cited by in corpus (7)

• Sketched Ridge Regression: Optimization Perspective, Statistical Perspective, and Model Averaging
• Unbiased estimators for random design regression
• Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design
• Modern Subsampling Methods for Large-Scale Least Squares Regression
• A near-optimal algorithm for approximating the John Ellipsoid
• LowCon: A design-based subsampling approach in a misspecified linear modeL
• Gaussian Process Landmarking on Manifolds