Discovering Shared Function Structures with Adaptable Parameters for Multi-Level Modeling via Symbolic Regression

This work introduces Multi-Level Symbolic Regression (MSR), a novel algorithm that leverages the inherent grouping in multi-level (MuL) datasets to learn a single, interpretable function structure shared across groups while adapting numerical parameters to capture group-specific variations. MSR runs parallel symbolic regression processes on each group in MuL datasets, fuses their outputs and balances performance across groups even in the presence of noise or unequal group sizes. To extend the applicability of our approach to standard tabular datasets lacking an explicit grouping variable, we also propose the Mean Local Intraclass Correlation Coefficient (MLICC). MLICC effectively identifies the most suitable feature to act as a level by partitioning data into local regions and quantifying intra-group similarity, thus facilitating implicit MuL analysis. Extensive experiments on both synthetic benchmarks and diverse real-world datasets ranging from educational and medical data to financial time series, which we collate and term as MSR-Bench, demonstrate that MSR achieves higher recovery rates of the true function structure and lower prediction errors compared to state-of-the-art symbolic regression methods and traditional MuL models. This Hot-of-the-Press paper summarizes the work K.S. Fong and M. Motani, "Multi-Level Symbolic Regression: Function Structure Learning for Multi-Level Data", International Conference on Artificial Intelligence and Statistics (AISTATS'24).