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The high-order Boltzmann machine: learned distribution and topology
F X Albizuri1, A Danjou, M Grana
1Dept. of Comput. Sci. and Artificial Intelligence, Univ. of the Basque Country, San Sebastian.
IEEE Transactions on Neural Networks
|January 1, 1995
Summary
This study formally defines high-order Boltzmann machines (BMs) and extends convergence results for their learning algorithms. It characterizes the probability distribution learned by high-order BMs using the Bahadur-Lazarsfeld expansion.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Statistical Modeling
Background:
- The Boltzmann machine (BM) is a generative stochastic neural network.
- Convergence properties of learning algorithms for two-order BMs are well-established.
- Extending these properties to higher-order BMs is a significant research challenge.
Purpose of the Study:
- To formally define the high-order Boltzmann machine (BM).
- To extend convergence results of learning algorithms for two-order BMs to high-order BMs.
- To characterize the probability distribution learned by high-order BMs and provide a criterion for determining BM topology.
Main Methods:
- Formal definition of high-order Boltzmann machines.
- Extension of convergence analysis for learning algorithms.
- Application of the Bahadur-Lazarsfeld expansion to characterize probability distributions.
- Development of a criterion based on significant correlations for topology selection.
Main Results:
- A formal definition for high-order Boltzmann machines is provided.
- Convergence properties of learning algorithms are extended to high-order BMs.
- The probability distribution learned by high-order BMs is characterized.
- A criterion for establishing BM topology based on distribution correlations is presented.
Conclusions:
- The study provides a theoretical framework for high-order Boltzmann machines.
- The findings facilitate a deeper understanding of the learning dynamics and representational capacity of higher-order BMs.
- The developed criterion aids in designing appropriate BM architectures for specific probability distributions.
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