Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models
Sean Plummer1, Debdeep Pati1, Anirban Bhattacharya1
1Department of Statistics, Texas A&M University, College Station, TX 77843, USA.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study analyzes coordinate ascent algorithms for Bayesian inference, revealing distinct convergence behaviors between sequential and parallel versions, especially in non-convex scenarios. Parameter expansion enhances convergence to global optima.
Area of Science:
- Computational Physics
- Statistical Mechanics
- Bayesian Inference
Background:
- Variational algorithms offer scalable Bayesian inference.
- Coordinate ascent is a key optimization technique.
- Understanding algorithm dynamics is crucial for reliable inference.
Purpose of the Study:
- To analyze the convergence of coordinate ascent algorithms for mean field variational inference.
- To compare the dynamics of sequential and parallel coordinate ascent.
- To investigate the impact of parameter expansion on convergence.
Main Methods:
- Dynamical systems theory applied to coordinate ascent algorithms.
- Analysis of the Ising model on two nodes.
- Empirical investigation using parameter expansion (Edward-Sokal coupling).
Main Results:
- Both sequential and parallel algorithms converge in convex regimes.
- Non-convex regimes show differing dynamics: parallel version exhibits oscillations.
- Parameter expansion enlarges the convergence region to global optima.
Conclusions:
- Sequential and parallel coordinate ascent exhibit distinct behaviors in non-convex settings.
- Parameter expansion is a valuable technique for improving variational inference convergence.
- Dynamical systems provide insights into the stability and convergence of variational algorithms.
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