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Full-Span Log-Linear Model and Fast Learning Algorithm.

Kazuya Takabatake1, Shotaro Akaho2

  • 1Human Informatics and Interaction Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, 305-8568, Japan k.takabatake@aist.go.jp.

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Summary
This summary is machine-generated.

The full-span log-linear (FSLL) model, a high-order Boltzmann machine, efficiently represents complex data distributions. It enables fast dual parameter computation and effective learning for small probabilistic models.

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Area of Science:

  • Machine Learning
  • Probabilistic Modeling
  • Statistical Inference

Background:

  • Boltzmann machines are powerful probabilistic models.
  • High-order interactions in data are challenging to model.
  • Efficient parameter computation and learning are crucial for practical applications.

Purpose of the Study:

  • Introduce the full-span log-linear (FSLL) model.
  • Demonstrate its capability to represent arbitrary positive distributions.
  • Develop an efficient learning algorithm for the FSLL model.

Main Methods:

  • The FSLL model is formulated as an nth order Boltzmann machine.
  • Dual parameters are computed in O(|X|log|X|) time.
  • An efficient learning algorithm is constructed using dual parameter properties.

Main Results:

  • The FSLL model has |X|-1 parameters and can represent any positive distribution.
  • Dual parameters are efficiently computable.
  • The model flexibly fits data without hyperparameter tuning.
  • Experiments showed successful learning of large datasets (|X|=220) within minutes.

Conclusions:

  • The FSLL model offers a flexible and efficient approach for high-order Boltzmann machines.
  • It provides a practical solution for small probabilistic models.
  • The model's performance is validated through successful experimental learning.