Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Algebraic analysis for nonidentifiable learning machines.

S Watanabe1

  • 1P&I Laboratory, Tokyo Institute of Technology, Yokohama, 226-8503 Japan.

Neural Computation
|March 20, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Ischemia-induced impairment of 2-deoxyglucose uptake and CA1 field potentials in rat hippocampal slices: protection by 5-HT1A receptor agonists and 5-HT2 receptor antagonists.

European journal of pharmacology·1992
Same author

Effect of substance P on circadian rhythms of firing activity and the 2-deoxyglucose uptake in the rat suprachiasmatic nucleus in vitro.

Brain research·1992
Same author

Cancer mortality trends in Japan 1960-1990: three-dimensional graphical presentation.

Japanese journal of clinical oncology·1992
Same author

Effect of time of day on adaptive response to a 4-week aerobic exercise program.

The Journal of sports medicine and physical fitness·1992
Same author

[A case of hepatic hydrothorax treated by pleuro-venous shunt].

Kyobu geka. The Japanese journal of thoracic surgery·1992
Same author

Type 3 GM1 gangliosidosis: characteristic MRI findings correlated with dystonia.

Acta neurologica Scandinavica·1992
Same journal

A Model-Free Reinforcement Learning Implementation of Decision Making Under Uncertainty by Sequential Sampling.

Neural computation·2026
Same journal

DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning.

Neural computation·2026
Same journal

Hierarchical Active Inference Using Successor Representations.

Neural computation·2026
Same journal

W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators.

Neural computation·2026
Same journal

A Hidden Markov Model-Inspired Sequence Classification Method for Hyperdimensional Computing.

Neural computation·2026
Same journal

Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics.

Neural computation·2026
See all related articles

This study reveals how the algebraic geometry of unidentifiable learning machines, like neural networks, impacts their learning curve. It proves Bayesian stochastic complexity relates to singularities, offering insights for better machine learning models.

Area of Science:

  • Machine Learning
  • Computational Algebraic Geometry
  • Statistical Learning Theory

Background:

  • Unidentifiable learning machines, such as multilayer neural networks, possess complex parameter spaces with singularities.
  • The learning curve and generalization error are critical metrics for evaluating machine learning model performance.
  • Understanding the relationship between model complexity and learning performance is crucial for developing effective AI.

Purpose of the Study:

  • To elucidate the connection between the algebraic geometrical structure of unidentifiable learning machines and their learning curves.
  • To rigorously derive the asymptotic behavior of Bayesian stochastic complexity (free energy) for such models.
  • To develop an algorithm for calculating key parameters related to singularities in the model's parameter space.

Related Experiment Videos

Main Methods:

  • Utilizing concepts from algebraic analysis to rigorously prove asymptotic formulas.
  • Applying principles of algebraic geometry, specifically the resolution of singularities.
  • Analyzing the structure of the parameter space for unidentifiable learning machines.

Main Results:

  • Established an asymptotic formula for Bayesian stochastic complexity: lambda(1) log n - (m(1) - 1) log log n + constant.
  • Identified lambda(1) and m(1) as birational invariants of singularities in the parameter space.
  • Demonstrated that non-regular models (e.g., multilayer networks) exhibit different complexity scaling compared to regular statistical models.

Conclusions:

  • Non-regular models, characterized by singularities, can be superior to regular models when employing Bayesian ensemble learning.
  • The derived parameters lambda(1) and m(1) provide quantitative measures of model complexity and learning behavior.
  • This research offers a rigorous mathematical framework for understanding generalization error in complex machine learning models.