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Alternating minimization and Boltzmann machine learning.

¹Dept. of Electr. Eng., Maryland Univ., College Park, MD.

IEEE Transactions on Neural Networks

|January 1, 1992

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Information geometry and alternating minimization offer a novel approach to training Boltzmann machines with hidden units. This method reveals close ties to gradient descent and the Expectation-Maximization algorithm.

Area of Science:

Machine Learning
Information Geometry
Statistical Modeling

Background:

Boltzmann machines are probabilistic models with applications in pattern recognition and AI.
Training Boltzmann machines, especially with hidden units, presents significant computational challenges.
Existing training methods often rely on approximations or complex optimization techniques.

Purpose of the Study:

To introduce an information geometry-based approach for training Boltzmann machines with hidden units.
To establish the relationship between this new method, gradient descent, and the Expectation-Maximization (EM) algorithm.
To present an iterative proportional fitting procedure for training Boltzmann machines without hidden units.

Main Methods:

Utilizing information divergence and alternating minimization for training Boltzmann machines.

Related Experiment Videos

Developing a novel algorithm derived from information geometry principles.

Incorporating an iterative proportional fitting procedure into the alternating minimization framework.

Main Results:

The proposed algorithm is shown to be closely related to gradient descent Boltzmann machine learning rules.
The connection between the new method, gradient descent, and the EM algorithm is clearly described.
An effective iterative proportional fitting procedure is presented for training machines without hidden units.

Conclusions:

Information geometry provides a robust framework for Boltzmann machine training.
The alternating minimization approach offers an efficient and theoretically grounded training method.
The study unifies several training paradigms for Boltzmann machines, including those with and without hidden units.