[Paper Review] On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models

Yining Wang, Adams Wei Yu+1 more|arXiv (Cornell University)|Jan 1, 2017

Optimal Experimental Design Methods19 citations

TL;DR

This paper proposes computationally efficient algorithms for selecting optimal experiment settings in measurement-constrained regression models, using continuous relaxation of combinatorial optimization followed by sampling or greedy post-processing. It establishes formal approximation guarantees and demonstrates strong performance on synthetic and real-world data across linear, generalized linear, and Delta-method 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.

Motivation & Objective

• To address the challenge of selecting a small, informative subset of experiment settings from a large pool of candidate designs.
• To overcome the computational intractability of combinatorial optimization in experiment selection under measurement constraints.
• To extend the proposed framework beyond linear regression to generalized linear models and Delta's method for estimating functions.
• To provide formal approximation guarantees for the selection algorithms while maintaining computational tractability.

Proposed method

• Formulate experiment selection as a combinatorial optimization problem constrained by measurement budgets.
• Relax the discrete selection problem into a continuous optimization problem using convex relaxation techniques.
• Apply sampling or greedy procedures as post-processing steps to recover discrete, actionable experiment sets from the relaxed solution.
• Establish theoretical approximation guarantees for both sampling and greedy post-processing strategies.
• Adapt the framework to generalized linear models and Delta's method by leveraging score functions and estimating equations.
• Use continuous relaxation to make otherwise intractable selection problems solvable in polynomial time.

Experimental results

Research questions

• RQ1 Can we design a computationally tractable method for selecting a small subset of experiment settings that maximizes information gain under measurement constraints?
• RQ2 How well do sampling and greedy post-processing strategies approximate the optimal discrete solution after continuous relaxation?
• RQ3 To what extent can the proposed framework be extended to generalized linear models and Delta's method for estimating functions?
• RQ4 What theoretical approximation guarantees can be established for the resulting algorithms?
• RQ5 How do the proposed methods compare in practice to baseline approaches on synthetic and real-world datasets?

Key findings

• The continuous relaxation approach enables efficient computation of near-optimal experiment selections in polynomial time.
• Both sampling and greedy post-processing strategies achieve formal approximation guarantees relative to the optimal discrete solution.
• The method effectively extends to generalized linear models and Delta's method, broadening applicability beyond standard linear regression.
• Numerical results on synthetic data confirm the theoretical approximation bounds and algorithmic stability.
• Empirical evaluation on real-world datasets demonstrates superior performance in terms of estimation accuracy and efficiency compared to baseline methods.
• The framework maintains strong performance even when the number of candidate designs is large, highlighting scalability.