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Variational Inference via Rényi Bound Optimization and Multiple-Source Adaptation.

Dana Zalman Oshri1,2, Shai Fine2

  • 1School of Computer Science, Reichman University, Herzliya 4610101, Israel.

Entropy (Basel, Switzerland)
|October 28, 2023
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Summary

Researchers introduce a new Variational Rényi Log Upper bound (VRLU) and Variational Rényi Sandwich (VRS) method for variational inference. This approach improves upon existing bounds, offering tighter error bounds and enhanced performance in Multiple-Source Adaptation tasks.

Keywords:
Rényi divergencemultiple-source adaptationvariational inference

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Area of Science:

  • Machine Learning
  • Probabilistic Modeling
  • Optimization

Background:

  • Variational inference approximates probability densities via optimization, often by maximizing the Evidence Lower Bound (ELBO).
  • Existing methods like variational Rényi (VR) and chi-squared bounds, based on Monte Carlo approximation, suffer from underestimation or high variance.
  • These limitations hinder accurate density approximation in complex models.

Purpose of the Study:

  • Introduce a novel upper bound, the Variational Rényi Log Upper bound (VRLU), preserving the upper bound property under Monte Carlo approximation.
  • Develop a sandwiched variational inference method (Variational Rényi Sandwich - VRS) for joint optimization of upper and lower bounds.
  • Evaluate the VRLU bound and VRS method against established techniques like Variational Autoencoders (VAE) and VR methods, particularly in Multiple-Source Adaptation (MSA).

Main Methods:

  • Proposed the Variational Rényi Log Upper bound (VRLU) as an improvement over existing variational bounds.
  • Developed the Variational Rényi Sandwich (VRS) method for simultaneous optimization of upper and lower bounds.
  • Conducted experiments comparing VRLU and VRS against VAE and VR methods, including theoretical and empirical analysis for MSA.

Main Results:

  • The VRLU bound maintains its upper bound property under Monte Carlo approximation, unlike prior bounds.
  • The VRS method demonstrates improved performance and tighter error bounds in Multiple-Source Adaptation tasks.
  • Empirical and theoretical results validate the effectiveness of VRS compared to leading MSA methods.

Conclusions:

  • The VRLU and VRS methods offer significant advancements in variational inference, addressing limitations of existing bounds.
  • VRS provides a robust framework for density estimation and domain adaptation, particularly in challenging Multiple-Source Adaptation scenarios.
  • The proposed methods show promise for improving predictive modeling in real-world applications with heterogeneous data sources.