On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models
This addresses the challenge of efficient experimental design in measurement-constrained regression for researchers and practitioners, but it is incremental as it builds on existing combinatorial optimization methods.
The paper tackles the problem of selecting a small subset of experiment settings from a large pool for linear regression models, deriving computationally tractable algorithms with formal approximation guarantees and demonstrating effectiveness on synthetic and real-world data.
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.