A Primer on Kolmogorov-Arnold Networks (KANs) for Probabilistic Time Series Forecasting

2025-10-19

AI Summary

Addressing the challenges of modeling nonlinear and heavy-tailed dynamics and weak uncertainty quantification in time series forecasting, this paper proposes P-KAN—the first probabilistic forecasting model built upon the Kolmogorov–Arnold network. Its core innovation replaces conventional scalar weights with learnable spline functions to directly parameterize Gaussian or Student’s *t* predictive distributions, achieving high expressivity with a lightweight architecture. This design eliminates the need for posterior approximation, significantly improving distributional calibration and robustness to outliers. Evaluated on satellite traffic forecasting, P-KAN outperforms MLP baselines with fewer parameters, delivering superior trade-offs among prediction accuracy, uncertainty quantification, and computational efficiency. The approach establishes a new paradigm for resource-constrained probabilistic time series modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and directly parameterizing predictive distributions, P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics. We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation. Results show that P-KANs consistently outperform Multi Layer Perceptron (MLP) baselines in both accuracy and calibration, achieving superior efficiency-risk trade-offs while using significantly fewer parameters. We build up P-KANs on two distributions, namely Gaussian and Student-t distributions. The Gaussian variant provides robust, conservative forecasts suitable for safety-critical scenarios, whereas the Student-t variant yields sharper distributions that improve efficiency under stable demand. These findings establish P-KANs as a powerful framework for probabilistic forecasting with direct applicability to satellite communications and other resource-constrained domains.

Problem

• Extends KANs for probabilistic time series forecasting
• Models nonlinear dynamics with spline-based functional connections
• Improves satellite traffic prediction accuracy and uncertainty calibration

Innovation

• Probabilistic KANs use spline-based functional connections
• Parameterize predictive distributions for uncertainty-aware forecasting
• Evaluate on Gaussian and Student-t distributions for efficiency