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Hyperlink regression via Bregman divergence.

Akifumi Okuno1, Hidetoshi Shimodaira2

  • 1RIKEN Center for Advanced Intelligence Project, Nihonbashi 1-4-1 Nihonbashi, Chuo-ku, Tokyo, 103-0027, Japan.

Neural Networks : the Official Journal of the International Neural Network Society
|April 16, 2020
PubMed
Summary

Bregman hyperlink regression (BHLR) introduces a unified framework for hyper-relational learning, predicting association strengths in data tuples. This method is statistically consistent and computationally tractable, offering theoretical guarantees for various existing techniques.

Keywords:
Bregman divergenceGraph embeddingHypernetworkNeural network

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Area of Science:

  • Machine Learning
  • Data Science
  • Statistical Modeling

Background:

  • Hyper-relational data involves U-tuples of data vectors with symmetric association strengths (hyperlink weights).
  • Existing methods for analyzing such data include logistic regression, Poisson regression, link prediction, and various factorization techniques.
  • Classical regression assumes independent and identically distributed (i.i.d.) data, which does not hold for hyper-relational datasets where tuples may share data vectors.

Purpose of the Study:

  • To propose Bregman hyperlink regression (BHLR), a general framework for hyper-relational learning.
  • To develop a method that learns a user-specified symmetric similarity function to predict hyperlink weights from data vectors.
  • To address theoretical challenges in hyper-relational data analysis and provide unified theoretical guarantees.

Main Methods:

  • BHLR minimizes the Bregman-divergence (BD) between observed hyperlink weights and estimated similarities for corresponding U-tuples.
  • The framework is flexible, accommodating various BD measures and nonlinear similarity functions (e.g., neural networks).
  • Statistical consistency and computational tractability are proven using stochastic optimization with a novel generalized minibatch sampling for hyper-relational data.

Main Results:

  • BHLR is shown to be statistically consistent, asymptotically recovering the true conditional expectation of hyperlink weights.
  • BHLR is computationally tractable, efficiently solvable via stochastic optimization algorithms.
  • The framework unifies and provides theoretical guarantees for several existing methods in link prediction and representation learning.

Conclusions:

  • Bregman hyperlink regression offers a unified, statistically sound, and computationally efficient approach to hyper-relational learning.
  • The proposed method generalizes and provides theoretical underpinnings for a wide range of existing machine learning techniques.
  • BHLR advances the analysis of complex relational data structures beyond traditional i.i.d. assumptions.