Variational Inference with Sequential Sample-Average Approximations: A Detailed Analysis

Core Concepts

VISA optimizes forward KL-divergence efficiently.

Abstract

The article introduces Variational Inference with Sequential Sample-Average Approximations (VISA) as a method for approximate inference in computationally intensive models. VISA extends importance-weighted forward-KL variational inference by using a sequence of sample-average approximations within a trust region. This allows for the reuse of model evaluations across multiple gradient steps, reducing computational cost. Experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and Pickover attractor demonstrate that VISA achieves comparable accuracy to standard methods with significant computational savings. The paper also discusses the background of variational inference, reparameterized VI, and importance-weighted forward-KL VI. It presents the algorithm for VISA and its implementation details. The results from experiments on different models show the effectiveness of VISA in achieving convergence with fewer model evaluations compared to traditional methods.

Stats

"VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more." "Savings of a factor two or more are realizable with conservatively chosen learning rates." "VISA requires fewer evaluations per gradient step compared to IWFVI."

Quotes

"VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more." "Savings of a factor two or more are realizable with conservatively chosen learning rates." "VISA requires fewer evaluations per gradient step compared to IWFVI."

Key Insights Distilled From

Variational Inference with Sequential Sample-Average Approximations

by Heiko Zimmer... at arxiv.org 03-15-2024

https://arxiv.org/pdf/2403.09429.pdf

Deeper Inquiries

How does underapproximation of posterior variance affect the performance of VISA

The underapproximation of posterior variance can have a significant impact on the performance of VISA. In reparameterized VI and IWFVI, this issue often arises due to the mode-seeking behavior of the reverse KL-divergence or low effective sample sizes leading to overfitting. Similarly, in VISA, keeping samples fixed for extended periods can result in overfitting to high-weight samples. This can lead to instability and collapsed variational distributions as the optimizer may repeatedly move towards these high-weight samples rather than exploring the full distribution. As a consequence, even small changes in the variational distribution could trigger drawing fresh samples more frequently than necessary.

What are the limitations when dealing with a large number of latent variables or parameters

When dealing with a large number of latent variables or parameters, VISA faces limitations that stem from its reliance on relatively few samples and infrequent refreshment of these samples during optimization. The method is not well-suited for models with numerous latent dimensions because it requires at least as many samples as there are latent dimensions for successful training. Additionally, optimizing SAAs using second-order methods like L-BGFS may amplify issues related to overfitting when dealing with a large number of parameters or latent variables. This limitation restricts VISA's applicability in scenarios where models involve complex structures with high-dimensional spaces.

How can second-order optimization methods be integrated into VISA for improved stability and convergence

Integrating second-order optimization methods into VISA could potentially enhance stability and convergence by leveraging curvature information during optimization. For instance, techniques like L-BFGS could be used within each SAA iteration to exploit second-order information efficiently while avoiding some pitfalls associated with first-order methods alone. By incorporating such methods judiciously into VISA's framework, it might be possible to address issues related to overfitting and improve convergence rates especially when dealing with challenging optimization landscapes involving multiple parameters or latent variables.