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Related Concept Videos

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Linearization and Approximation01:26

Linearization and Approximation

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Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Related Experiment Videos

Approximate learning algorithm in Boltzmann machines.

Muneki Yasuda1, Kazuyuki Tanaka

  • 1Graduate School of Information Sciences, Tohoku University, Sendai, Miyagi, Japan. muneki@smapip.is.tohoku.ac.jp

Neural Computation
|August 19, 2009
PubMed
Summary

We introduce new, practical learning algorithms for Boltzmann machines, a type of Markov random field. These methods use belief propagation and linear response approximation to address NP-hard learning problems.

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Area of Science:

  • Artificial Intelligence
  • Statistical Mechanics
  • Machine Learning

Background:

  • Boltzmann machines are Markov random fields, equivalent to Ising spin models for binary cases.
  • Learning in Boltzmann machines is an NP-hard problem, necessitating approximate methods.

Purpose of the Study:

  • To propose novel and practical learning algorithms for Boltzmann machines.
  • To address the computational challenges of learning in these complex models.

Main Methods:

  • Utilizing the belief propagation algorithm.
  • Employing the linear response approximation, also known as advanced mean field methods.

Main Results:

  • Development of new, practical learning algorithms for Boltzmann machines.
  • Demonstration of the proposed algorithm's validity through numerical experiments.

Conclusions:

  • The proposed belief propagation and linear response approximation methods offer a practical solution for Boltzmann machine learning.
  • These advanced mean field techniques effectively tackle the NP-hard learning problem in Boltzmann machines.