HierBOSSS: Hierarchical Bayesian Operator-induced Symbolic Regression Trees for Structural Learning of Scientific Expressions

This repository holds the source code and implementation of HierBOSSS for Bayesian structural learning of scientific symbolic expressions proposed in Roy, S., Dey, P., Pati, D., & Mallick, B. K. (2025+), Hierarchical Bayesian Operator-induced Symbolic Regression Trees for Structural Learning of Scientific Expressions.

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Developers and Maintainers

Somjit Roy
Department of Statistics
Texas A&M University, College Station, TX, USA

📧 Email: sroy_123@tamu.edu
🌐 Website: https://roy-sr-007.github.io

Pritam Dey
Department of Statistics
Texas A&M University, College Station, TX, USA

📧 Email: pritam.dey@tamu.edu
🌐 Website: https://pritamdey.github.io

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Overview

We develop a hierarchical Bayesian framework for symbolic regression (HierBOSSS) that models symbolic expressions through an ensemble of symbolic tree-structured scientific expressions, regarded as the symbolic forest component. Conjugate priors are assigned to model regression parameters, while a regularizing prior is designed for the individual symbolic tree structures. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior–based criterion adhering to the Occam’s window principle.

HierBOSSS bridges the gap between SciML and Statistical AI in context of symbolic regression.

Figure 1: Symbolic tree representation of scientific expressions.