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Understanding Hierarchical Processes.

Wray Buntine1,2

  • 1College of Engineering and Computer Science, VinUniversity, Hanoi 100000, Vietnam.

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|December 23, 2022
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Summary
This summary is machine-generated.

This study introduces a general theory for hierarchical stochastic processes, extending properties of the hierarchical Dirichlet process to broader families like the gamma process. This advances statistical machine learning and deep neural network modeling.

Keywords:
Bayesian nonparametricsDirichet processPitman–Yor processgamma processhierarchical processnon-parametric LDA

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Area of Science:

  • Statistical Machine Learning
  • Probability Theory
  • Deep Neural Networks

Background:

  • Hierarchical stochastic processes, including the hierarchical Dirichlet process, are crucial for statistical machine learning and deep neural networks.
  • These models enable probability vector networks, facilitating information sharing.

Purpose of the Study:

  • To present a general theory of hierarchical stochastic processes.
  • To illustrate the application of this theory to the gamma process and the generalized gamma process.
  • To demonstrate the extension of desirable properties from hierarchical Dirichlet processes to a wider class of models.

Main Methods:

  • Developing a general theory for hierarchical stochastic processes.
  • Estimating moments of infinitely divisible distributions using cumulants.
  • Applying equivalences and relationships to networks of hierarchical processes.

Main Results:

  • The study establishes a general framework for hierarchical stochastic processes.
  • It shows that many beneficial properties of hierarchical Dirichlet processes are applicable to broader families.
  • Demonstrates applications using the gamma and generalized gamma processes.

Conclusions:

  • The generalized theory provides a unified approach to hierarchical stochastic processes.
  • This framework enhances capabilities in statistical modeling and non-parametric research.
  • The findings support the use of these processes in advanced machine learning applications.