(Exhaustive) Symbolic Regression and model selection by minimum description length
This addresses the problem of unreliable and poorly-justified function discovery in symbolic regression for scientists and researchers, offering a general-purpose methodology, though it is incremental as it builds on existing principles like minimum description length.
The authors tackled the challenges of traditional symbolic regression algorithms, which often fail to find good functions and rely on ambiguous selection procedures, by proposing an exhaustive search with model selection based on the minimum description length principle. The resulting algorithm identified many functions superior to literature standards in three astrophysics problems, such as the expansion history of the universe.
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown (and likely significant) probability of failing to find any given good function, and they suffer from ambiguity and poorly-justified assumptions in their function-selection procedure. To address these I propose an exhaustive search and model selection by the minimum description length principle, which allows accuracy and complexity to be directly traded off by measuring each in units of information. I showcase the resulting publicly available Exhaustive Symbolic Regression algorithm on three open problems in astrophysics: the expansion history of the universe, the effective behaviour of gravity in galaxies and the potential of the inflaton field. In each case the algorithm identifies many functions superior to the literature standards. This general purpose methodology should find widespread utility in science and beyond.