Adaptive Variational Inference: Beyond Bethe, Tree-Reweighted, and Convex Free Energies

Area of Science:

• Machine Learning
• Statistical Modeling
• Computational Statistics

Background:

• Variational inference is crucial for approximating key quantities in probabilistic graphical models.
• Existing methods like Bethe and tree-reweighted approximations are efficient but struggle with complex, interactive models.

Purpose of the Study:

• To analyze and generalize existing variational inference approximations.
• To introduce novel methods for automatically optimizing approximation parameters.
• To improve the accuracy of marginal distribution and partition function estimation.

Main Methods:

• Analysis of two generalized approximation classes: state energy modification and alternative entropy approximation.
• Development of ADAPT-c and ADAPT-zeta algorithms for automatic parameter tuning.
• Empirical evaluation on pairwise binary graphical models.

Main Results:

• Identification of favorable parameter regimes for the proposed approximations.
• Demonstration of ADAPT-c and ADAPT-zeta's effectiveness in enhancing approximation accuracy.
• Successful approximation of marginals and partition functions in experimental settings.

Conclusions:

• The proposed ADAPT-c and ADAPT-zeta methods offer significant improvements over traditional variational inference techniques.
• These methods provide a robust framework for handling complex probabilistic graphical models.
• The findings pave the way for more accurate and efficient analysis of large-scale probabilistic systems.