Guillaume Moinard

Etienne Russeil, Fabrício Olivetti de França, Konstantin Malanchev et al.

Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless, frequently, the researcher is confronted with multiple sets of results obtained from experiments conducted with different setups. Traditional SR methods may fail to find the underlying expression since the parameters of each experiment can be different. In this work we present Multi-View Symbolic Regression (MvSR), which takes into account multiple datasets simultaneously, mimicking experimental environments, and outputs a general parametric solution. This approach fits the evaluated expression to each independent dataset and returns a parametric family of functions f(x; theta) simultaneously capable of accurately fitting all datasets. We demonstrate the effectiveness of MvSR using data generated from known expressions, as well as real-world data from astronomy, chemistry and economy, for which an a priori analytical expression is not available. Results show that MvSR obtains the correct expression more frequently and is robust to hyperparameters change. In real-world data, it is able to grasp the group behavior, recovering known expressions from the literature as well as promising alternatives, thus enabling the use of SR to a large range of experimental scenarios.

Etienne Russeil, Fabrício Olivetti de França, Konstantin Malanchev et al.

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and careful observations. A modern alternative is to automate part of this process with symbolic regression (SR). The SR algorithms search for a function that adequately fits the observed data while trying to enforce sparsity, in the hopes of generating an interpretable equation. A particularly interesting extension to these algorithms is the Multi-view Symbolic Regression (MvSR). It searches for a parametric function capable of describing multiple datasets generated by the same phenomena, which helps to mitigate the common problems of overfitting and data scarcity. Recently, multiple implementations added support to MvSR with small differences between them. In this paper, we test and compare MvSR as supported in Operon, PySR, phy-SO, and eggp, in different real-world datasets. We show that they all often achieve good accuracy while proposing solutions with only few free parameters. However, we find that certain features enable a more frequent generation of better models. We conclude by providing guidelines for future MvSR developments.