Probabilistic Kolmogorov–Arnold Network: An Approach for Stochastic Modelling Using Divisive Data Re-Sorting

The Kolmogorov–Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally obtained datasets for regression models typically include uncertainties, which in some cases, cannot be neglected. The conventional way to account for the latter is to model confidence intervals of the systems’ outputs in addition to the expected values of the outputs. However, such information may be insufficient, and in some cases, researchers aim to obtain probability distributions of the outputs. The present paper proposes a method for estimating probability distributions of the outputs by constructing an ensemble of models. The suggested approach covers input-dependent probability distributions of the outputs and is capable of capturing the multi-modality, as well as the variation of the distribution type with the inputs. Although the method is applicable to any regression model, the present paper combines it with KANs, since their specific structure leads to the construction of computationally efficient models. The source codes are available online.