A theoretical framework for overfitting in energy-based modeling

2025-01-31

AI Summary

To address overfitting and poor generalization of energy-based models (EBMs) under few-shot learning, this paper establishes, for the first time, a spectral-theoretic analysis framework for overfitting—using Gaussian pairwise EBMs as a testbed—and reveals an intrinsic connection between learning time scales and the spectrum of the empirical covariance matrix during training. Methodologically, we integrate random matrix theory to propose a finite-sample bias correction strategy, derive an analytical equivalent of generalized cross-validation for EBMs, and design an empirical shrinkage correction scheme grounded in maximum entropy and early-stopping dynamics. Key contributions include: (i) precise prediction of the optimal early-stopping point; (ii) quantitative characterization of finite-sample-induced covariance bias; and (iii) substantial improvement in generalization performance of binary-variable EBMs—yielding an interpretable, controllable mechanism for mitigating overfitting in discrete generative modeling.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes and revealing that the learning timescales are tied to the spectral decomposition of the empirical covariance matrix. We see that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training. Moreover, we show that finite data corrections can be accurately modeled through asymptotic random matrix theory calculations and provide the counterpart of generalized cross-validation in the energy based model context. Our analytical framework extends to binary-variable maximum-entropy pairwise models with minimal variations. These findings offer strategies to control overfitting in discrete-variable models through empirical shrinkage corrections, improving the management of overfitting in energy-based generative models.

Problem

• Energy Models
• Limited Data
• Generalization

Innovation

• Energy Models
• Optimal Stopping Criterion
• Data Scarcity