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Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the...
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Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines.

Aurelien Decelle1,2, Sungmin Hwang3, Jacopo Rocchi3

  • 1Laboratoire Interdisciplinaire des Sciences du Numérique, Université Paris-Saclay, CNRS, INRIA TAU team, 91190, Gif-sur-Yvette, France.

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|October 8, 2021
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Summary
This summary is machine-generated.

We developed an efficient algorithm using Thouless-Anderson-Palmer (TAP) equations for inverse problems with clustered data. This method successfully retrieves original patterns and scales to large systems, outperforming existing techniques.

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Area of Science:

  • Statistical physics
  • Machine learning
  • Computational neuroscience

Background:

  • Inverse problems with binary clustered data are challenging.
  • Existing methods like mean-field and pseudo-likelihood have limitations.
  • The Hopfield model in a teacher-student scenario presents such a challenge during retrieval.

Purpose of the Study:

  • To propose an efficient algorithm for solving inverse problems with binary clustered datasets.
  • To retrieve original patterns from teacher datasets.
  • To enable application to large system sizes.

Main Methods:

  • Estimation of the posterior using Thouless-Anderson-Palmer (TAP) equations.
  • A parallel updating scheme for efficient computation.
  • Comparison with Restricted Boltzmann Machine (RBM) learning.

Main Results:

  • The proposed algorithm successfully retrieves original teacher patterns.
  • The parallel updating scheme allows for scalability to large system sizes.
  • Analogies and differences with RBM learning were identified.

Conclusions:

  • The TAP-based parallel updating algorithm is an efficient solution for inverse problems with clustered data.
  • This method offers advantages in pattern retrieval and scalability.
  • It provides a valuable alternative to existing approaches like RBMs.