Marginalised Normal Regression: Unbiased curve fitting in the presence of x-errors
ArXiv 2309.00948 (2023)
Constraints on dark matter and astrophysics from tomographic $γ$-ray cross-correlations
ArXiv 2307.14881 (2023)
Priors For Symbolic Regression
GECCO 2023 Companion - Proceedings of the 2023 Genetic and Evolutionary Computation Conference Companion (2023) 2402-2411
Abstract:
When choosing between competing symbolic models for a data set, a human will naturally prefer the “simpler” expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a ngram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.Modeling and testing screening mechanisms in the laboratory and in space
ArXiv 2305.18899 (2023)