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Information Theory in Emerging Machine Learning Techniques

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 15 March 2025 | Viewed by 405

Special Issue Editor


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Guest Editor
1. Data61, CSIRO, Eveleigh, NSW 2015, Australia
2. School of Computing, Australian National University, Canberra, ACT 2601, Australia
Interests: machine learning; information geometry; deep learning; model selection; dimensionality reduction; manifold learning

Special Issue Information

Dear Colleagues,

In the past two decades, deep learning, as part of machine learning, has undergone significant development. Many emerging techniques have achieved state-of-the-art performance across diverse learning tasks and areas of application, such as natural language processing, robotics, multimedia processing, and healthcare. However, many of these new methods are based on empirical evidence. While theoretical machine learning and its relationships with information theory are well developed, the theoretical analysis for deep learning has not kept pace with the engineering advancements of new learning mechanisms.

There are substantial aspects of deep learning that are not common in other areas, like its unique properties of generalization, representation learning, and latent features, its interaction with optimization, generalization and over-parameterization, layer-wise aspects of the representation, stability, and robustness. These provide a rich foundation for the application and use of information theory.

Information theory has been fundamental to modern machine learning and can significantly contribute to the development of deep learning theory. This Special Issue aims to (1) provide information-theoretical insights into new deep learning methods and (2) develop new deep learning mechanisms, or adapt current mechanisms grounded in information theory. Its focus on emerging machine learning techniques indicates a particular interest in cutting-edge deep learning techniques that have not been analyzed previously and have not been examined through simplified architectures.

Dr. Ke Sun
Guest Editor

Manuscript Submission Information

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Keywords

  • deep learning
  • information theory
  • information divergence
  • Riemannian geometry
  • Fisher information
  • information bottleneck
  • deep autoencoders
  • normalization in deep learning
  • deep neural network optimizers

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Published Papers (1 paper)

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Research

29 pages, 1916 KiB  
Article
Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center
by Frank Nielsen
Entropy 2024, 26(12), 1008; https://doi.org/10.3390/e26121008 - 22 Nov 2024
Abstract
The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the [...] Read more.
The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the Jeffreys centroid is not available in closed form for sets of categorical or multivariate normal distributions, two widely used statistical models, and thus needs to be approximated numerically in practice. In this paper, we first propose the new Jeffreys–Fisher–Rao center defined as the Fisher–Rao midpoint of the sided Kullback–Leibler centroids as a plug-in replacement of the Jeffreys centroid. This Jeffreys–Fisher–Rao center admits a generic formula for uni-parameter exponential family distributions and a closed-form formula for categorical and multivariate normal distributions; it matches exactly the Jeffreys centroid for same-mean normal distributions and is experimentally observed in practice to be close to the Jeffreys centroid. Second, we define a new type of inductive center generalizing the principle of the Gauss arithmetic–geometric double sequence mean for pairs of densities of any given exponential family. This new Gauss–Bregman center is shown experimentally to approximate very well the Jeffreys centroid and is suggested to be used as a replacement for the Jeffreys centroid when the Jeffreys–Fisher–Rao center is not available in closed form. Furthermore, this inductive center always converges and matches the Jeffreys centroid for sets of same-mean normal distributions. We report on our experiments, which first demonstrate how well the closed-form formula of the Jeffreys–Fisher–Rao center for categorical distributions approximates the costly numerical Jeffreys centroid, which relies on the Lambert W function, and second show the fast convergence of the Gauss–Bregman double sequences, which can approximate closely the Jeffreys centroid when truncated to a first few iterations. Finally, we conclude this work by reinterpreting these fast proxy Jeffreys–Fisher–Rao and Gauss–Bregman centers of Jeffreys centroids under the lens of dually flat spaces in information geometry. Full article
(This article belongs to the Special Issue Information Theory in Emerging Machine Learning Techniques)
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