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From Bilinear Regression to Inductive Matrix Completion: A Quasi-Bayesian Analysis.

The Tien Mai1

  • 1Department of Mathematical Sciences, Norwegian University of Science and Technology, 7034 Trondheim, Norway.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary

This study introduces a novel Bayesian quasi-likelihood method for bilinear regression with missing data, enhancing inductive matrix completion. Numerical studies demonstrate its effectiveness in handling complex data relationships.

Keywords:
Langevin Monte CarloPAC-Bayesian boundbilinear regressionlow-rank modelmatrix completion

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Bilinear regression models complex relationships between multiple variables and responses.
  • Inductive matrix completion addresses missing data in response matrices, a common challenge.

Purpose of the Study:

  • To develop a robust statistical method for bilinear regression with missing data.
  • To adapt Bayesian statistics and quasi-likelihood for inductive matrix completion.
  • To provide theoretical guarantees and efficient computation for the proposed estimators.

Main Methods:

  • A quasi-Bayesian approach combining quasi-likelihood for bilinear regression.
  • Leveraging low-rankness assumption and PAC-Bayes bounds for inductive matrix completion.
  • Employing Langevin Monte Carlo for computationally efficient estimator computation.

Main Results:

  • The proposed method effectively handles complex relationships in bilinear regression.
  • Statistical properties of estimators and quasi-posteriors are established using PAC-Bayes bounds.
  • Numerical studies validate the performance and efficiency of the approach.

Conclusions:

  • The novel Bayesian quasi-likelihood method offers a robust solution for bilinear regression with missing data.
  • The approach provides theoretical insights and practical computational efficiency for inductive matrix completion.
  • The method demonstrates strong performance across various conditions in numerical evaluations.