Probabilistic Kolmogorov-Arnold Network
Andrew Polar, Michael Poluektov

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…
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Taxonomy
TopicsNeural Networks and Applications
