Probabilistic Kolmogorov-Arnold Network

TL;DR

This paper introduces a probabilistic extension to Kolmogorov-Arnold networks (KANs) that estimates input-dependent output distributions, capturing multi-modality and distribution variation, thus enhancing regression models with uncertainty quantification.

Contribution

It presents a novel method for estimating input-dependent probability distributions in regression, integrated with KANs for computational efficiency.

Findings

Method captures multi-modal output distributions.

Enables input-dependent uncertainty modeling.

Applicable to various regression models.

Abstract

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 in the case of aleatoric uncertainty (i.e. for systems that produce different outputs each time an experiment is executed with the same inputs). 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 the specific structure of KANs leads to computationally-efficient models' construction. The source code is available online.