Bayesian Experimental Design for Symbolic Discovery

TL;DR

This paper develops a Bayesian optimal experimental design framework for symbolic discovery, optimizing data collection to improve inference of functional models using advanced sampling and numerical methods.

Contribution

It introduces a novel application of Bayesian experimental design to symbolic discovery, integrating Hamiltonian Monte Carlo and convolution techniques for efficient inference.

Findings

Effective optimization of experimental design criteria.

Successful application of Hamiltonian Monte Carlo sampling.

Use of numerical and fast transform methods for predictive distribution computation.

Abstract

This study concerns the formulation and application of Bayesian optimal experimental design to symbolic discovery, which is the inference from observational data of predictive models taking general functional forms. We apply constrained first-order methods to optimize an appropriate selection criterion, using Hamiltonian Monte Carlo to sample from the prior. A step for computing the predictive distribution, involving convolution, is computed via either numerical integration, or via fast transform methods.