A kinetic-based regularization method for data science applications

2025-03-06

AI Summary

This paper addresses the degradation in interpolation and regression accuracy for function learning on high-dimensional noisy data, caused by representational mismatch between discrete sampling and continuous modeling. We propose a kinetic-energy-inspired regularization method grounded in statistical mechanics: parameter optimization is formulated as an energy-minimization process, with constraints imposed on low-order moments of the data distribution to enforce consistency between discrete samples and their continuous limit. The method requires no empirical hyperparameter tuning, exhibits robustness to noise, scales effectively to high dimensions, and supports efficient local computation. It represents the first integration of dynamical-systems principles into regularization frameworks for function learning. Experiments demonstrate substantial improvements over baselines—including RBF—on both interpolation and regression tasks, particularly under high-dimensional and strongly noisy conditions. Moreover, it significantly reduces computational complexity and memory overhead.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.

Problem

• Develops a physics-based regularization for function learning.
• Improves interpolation and regression accuracy in high dimensions.
• Enhances computational efficiency for large, noisy datasets.

Innovation

• Physics-based regularization for function learning
• Minimizes discrepancy between discrete and continuum data
• Computationally efficient, no empirical parameter tuning