Function Class Learning with Genetic Programming: Towards Explainable Meta Learning for Tumor Growth Functionals

Paragangliomas are rare, primarily slow-growing tumors for which the underlying growth pattern is unknown. Therefore, determining the best care for a patient is hard. Currently, if no significant tumor growth is observed, treatment is often delayed, as treatment itself is not without risk. However, by doing so, the risk of (irreversible) adverse effects due to tumor growth may increase. Being able to predict the growth accurately could assist in determining whether a patient will need treatment during their lifetime and, if so, the timing of this treatment. The aim of this work is to learn the general underlying growth pattern of paragangliomas from multiple tumor growth data sets, in which each data set contains a tumor's volume over time. To do so, we propose a novel approach based on genetic programming to learn a function class, i.e., a parameterized function that can be fit anew for each tumor. We do so in a unique, multi-modal, multi-objective fashion to find multiple potentially interesting function classes in a single run. We evaluate our approach on a synthetic and a real-world data set. By analyzing the resulting function classes, we can effectively explain the general patterns in the data.

Multi-modal multi-objective model-based genetic programming to find multiple diverse high-quality models

Explainable artificial intelligence (XAI) is an important and rapidly expanding research topic. The goal of XAI is to gain trust in a machine learning (ML) model through clear insights into how the model arrives at its predictions. Genetic programming (GP) is often cited as being uniquely well-suited to contribute to XAI because of its capacity to learn (small) symbolic models that have the potential to be interpreted. Nevertheless, like many ML algorithms, GP typically results in a single best model. However, in practice, the best model in terms of training error may well not be the most suitable one as judged by a domain expert for various reasons, including overfitting, multiple different models existing that have similar accuracy, and unwanted errors on particular data points due to typical accuracy measures like mean squared error. Hence, to increase chances that domain experts deem a resulting model plausible, it becomes important to be able to explicitly search for multiple, diverse, high-quality models that trade-off different meanings of accuracy. In this paper, we achieve exactly this with a novel multi-modal multi-tree multi-objective GP approach that extends a modern model-based GP algorithm known as GP-GOMEA that is already effective at searching for small expressions.