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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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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Active Inference, Belief Propagation, and the Bethe Approximation.

Sarah Schwöbel1, Stefan Kiebel2, Dimitrije Marković3

  • 1Department of Psychology, Technische Universität Dresden, Dresden 01187, Germany sarah.schwoebel@tu-dresden.de.

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Summary
This summary is machine-generated.

Planning as inference uses approximations. The Bethe approximation, unlike mean-field, captures dependencies, improving goal-directed behavior and agent predictions in complex tasks.

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Area of Science:

  • Computational Neuroscience
  • Machine Learning
  • Cognitive Science

Background:

  • Planning in goal-directed behavior is modeled as an inference process.
  • Active inference previously used a mean-field approximation for planning.
  • Mean-field approximation assumes variable independence, leading to overconfidence and local minima.

Purpose of the Study:

  • Reformulate active inference using the Bethe approximation.
  • Incorporate pairwise statistical dependencies for improved environmental modeling.
  • Enhance planning accuracy in goal-directed behavior.

Main Methods:

  • Applied the Bethe approximation to the active inference framework.
  • Utilized belief propagation as the minimizer of variational free energy.
  • Simulated agent behavior in a goal-reaching task with uncertainties.

Main Results:

  • The Bethe approximation allows for pairwise statistical dependencies.
  • Bethe approximation-based agents showed higher success rates in goal-reaching tasks.
  • Bethe agents exhibited more accurate predictions of action consequences.

Conclusions:

  • The Bethe approximation improves active inference for complex tasks.
  • Capturing statistical dependencies enhances agent performance.
  • Active inference with Bethe approximation broadens its applicability.