Statistical Mechanics of Learning: A Variational Approach for Real Data

2002/08/19 by D. Malzahn, Dörthe Malzahn, Manfred Opper +1 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #cond-mat.dis-nn #physics.data-an

paper · pdf · doi:10.1103/physrevlett.89.108302

published as Phys. Rev. Lett. 89 (10), 108302 (2002) · 4 pages, 2 figures

openalex publication_date 2002/08/19 · arxiv created 2002/09/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators for generalization errors that are based on training data alone.

Citations

• The space of interactions in neural network models
• Field Theories for Learning Probability Distributions

Cited by

• Learning curves for multi-task Gaussian process regression