Symbolic regression (SR) 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 subtasks 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 SR algorithms on these benchmarks and present an in-depth analysis of the results, discuss current challenges of SR algorithms and highlight possible improvements for the benchmark itself.

There is growing interest in monitoring gait patterns in people with neurological conditions. The democratisation of wearable inertial sensors has enabled the study of gait in free living environments. One pivotal aspect of gait assessment in uncontrolled environments is the ability to accurately recognise gait instances. Previous work has focused on wavelet transform methods or general machine learning models to detect gait; the former assume a comparable gait pattern between people and the latter assume training datasets that represent a diverse population. In this paper, we argue that these approaches are unsuitable for people with severe motor impairments and their distinct gait patterns, and make the case for a lightweight personalised alternative. We propose an approach that builds on top of a general model, fine-tuning it with personalised data. A comparative proof-of-concept evaluation with general machine learning (NN and CNN) approaches and personalised counterparts showed that the latter improved the overall accuracy in 3.5% for the NN and 5.3% for the CNN. More importantly, participants that were ill-represented by the general model (the most extreme cases) had the recognition of gait instances improved by up to 16.9% for NN and 20.5% for CNN with the personalised approaches. It is common to say that people with neurological conditions, such as Parkinson’s disease, present very individual motor patterns, and that in a sense they are all outliers; we expect that our results will motivate researchers to explore alternative approaches that value personalisation rather than harvesting datasets that are may be able to represent these differences.

The representation of individuals in Genetic Programming (GP) has a large impact on the evolutionary process. In previous work, we investigated the evolutionary process of three Grammar-Guided GP (GGGP) methods, Context-Free Grammars GP (CFG-GP), Grammatical Evolution (GE) and Structured Grammatical Evolution (SGE), in the context of the complex, real-world problem of predicting the glucose level of people with diabetes two hours ahead of time. We concluded that representation choice is more impactful with a higher maximum depth, and that CFG-GP better explores the search space for deeper trees, achieving better results. Furthermore, we find that CFG-GP relies more on feature construction, whereas GE and SGE rely more on feature selection. Additionally, we altered the GGGP methods in two ways: using $$\epsilon$$ ϵ -lexicase selection, which solved the overfitting problem of CFG-GP and helps it to adapt to patients with high glucose variability; and with a penalization of complex trees, to create more interpretable trees. Combining $$\epsilon$$ ϵ -lexicase selection with CFG-GP performed best. In this work, we extend on the previous work and evaluated the impact of initialization methods in the quality of solutions. We found that they have no significant impact, even when the change of representation has.