Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main promise of this approach is that it may return an interpretable model that can be insightful to users, while maintaining high accuracy. The current standard for benchmarking these algorithms is SRBench, which evaluates methods on hundreds of datasets that are a mix of real-world and simulated processes spanning multiple domains. At present, the ability of SRBench to evaluate interpretability is limited to measuring the size of expressions on real-world data, and the exactness of model forms on synthetic data. In practice, model size is only one of many factors used by subject experts to determine how interpretable a model truly is. Furthermore, SRBench does not characterize algorithm performance on specific, challenging sub-tasks of regression such as feature selection and evasion of local minima. In this work, we propose and evaluate an approach to benchmarking SR algorithms that addresses these limitations of SRBench by 1) incorporating expert evaluations of interpretability on a domain-specific task, and 2) evaluating algorithms over distinct properties of data science tasks. We evaluate 12 modern symbolic regression algorithms on these benchmarks and present an in-depth analysis of the results, discuss current challenges of symbolic regression algorithms and highlight possible improvements for the benchmark itself.

MOTIVATION: The identification of predictive biomarker signatures from omics and multi-omics data for clinical applications is an active area of research. Recent developments in assay technologies and machine learning (ML) methods have led to significant improvements in predictive performance. However, most high-performing ML methods suffer from complex architectures and lack interpretability. RESULTS: We present the application of a novel symbolic-regression-based algorithm, the QLattice, on a selection of clinical omics datasets. This approach generates parsimonious high-performing models that can both predict disease outcomes and reveal putative disease mechanisms, demonstrating the importance of selecting maximally relevant and minimally redundant features in omics-based machine-learning applications. The simplicity and high-predictive power of these biomarker signatures make them attractive tools for high-stakes applications in areas such as primary care, clinical decision-making and patient stratification. AVAILABILITY AND IMPLEMENTATION: The QLattice is available as part of a python package (feyn), which is available at the Python Package Index (https://pypi.org/project/feyn/) and can be installed via pip. The documentation provides guides, tutorials and the API reference (https://docs.abzu.ai/). All code and data used to generate the models and plots discussed in this work can be found in https://github.com/abzu-ai/QLattice-clinical-omics. SUPPLEMENTARY INFORMATION: Supplementary material is available at Bioinformatics online.