VISA: Variational Inference with Sequential Sample-Average Approximations

Core Concepts

VISA optimizes variational inference efficiently by reusing samples, reducing computational cost.

Abstract

Abstract VISA introduces a method for approximate inference in computationally intensive models. It extends importance-weighted forward-KL variational inference by employing sequential sample-average approximations. Introduction Bayesian analysis in simulation-based models is computationally costly due to repeated model evaluations. Gradient-based methods are commonly used for inference in such models. Data Extraction "VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more." Background Variational Inference (VI) approximates an intractable target density with a tractable variational distribution. SAA for Forward-KL Variational Inference Sample-average approximations are used to approximate expected loss with a surrogate loss in optimization problems. Experiments VISA is compared to IWFVI in terms of inference quality and the number of model evaluations across different experiments. Related Work Recent work studies SAAs in the context of variational inference, focusing on optimizing reverse KL-divergence and using second-order methods. Pickover Attractor Experiment The Pickover attractor model is used to evaluate VISA's performance, showing stable convergence with fewer samples compared to IWFVI.

Stats

"VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more."

Quotes

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 the use of sequential sample-average approximations impact the scalability of VISA for models with a large number of latent variables

VISA's scalability for models with a large number of latent variables is impacted by the use of sequential sample-average approximations in several ways. Firstly, as the number of latent variables increases, maintaining a fixed set of samples for each SAA iteration may become computationally intensive. The need to refresh samples based on ESS thresholds can lead to increased computational overhead, especially when dealing with high-dimensional spaces where evaluating the model is already resource-intensive. Additionally, larger latent variable spaces may require more frequent updates to the proposal distribution parameters and trust regions, further adding to the computational complexity.

What are the potential limitations or challenges faced when applying VISA to models that require high-dimensional parameter spaces

When applying VISA to models that necessitate high-dimensional parameter spaces, several potential limitations and challenges may arise. One significant challenge is related to sampling efficiency and coverage within these high-dimensional spaces. As the dimensionality increases, maintaining an adequate representation of the posterior distribution becomes increasingly difficult due to sparsity issues and curse of dimensionality effects. This can result in suboptimal convergence rates and potentially biased estimates if not addressed appropriately. Moreover, optimizing variational objectives in high-dimensional parameter spaces requires careful tuning of hyperparameters such as learning rates and ESS thresholds. The interplay between these hyperparameters becomes more intricate as dimensionality grows, making it challenging to strike a balance between exploration and exploitation effectively. Furthermore, interpreting results from VISA in high-dimensional settings can be complex due to difficulties in visualizing or comprehending multi-dimensional distributions accurately. Ensuring robustness against overfitting while capturing essential features of the posterior distribution poses additional challenges when dealing with vast parameter spaces.

How might the concept of trust regions be extended or adapted for other types of probabilistic programming systems beyond those discussed in this content

The concept of trust regions used in VISA could be extended or adapted for other probabilistic programming systems beyond those discussed in this context by incorporating domain-specific knowledge or constraints into defining trust region boundaries. For instance: In hierarchical Bayesian models where certain parameters are known or expected to exhibit specific relationships (e.g., correlations), customized trust region definitions could enforce these constraints during optimization. For models involving structured data representations like graphs or time series data, trust regions could be tailored based on graph properties or temporal dependencies. Trust regions might also be adapted based on prior information about certain parameters' ranges or distributions within specific application domains. By integrating such domain-specific considerations into defining trust regions within probabilistic programming systems outside traditional settings like VI-based methods discussed here,VISA's adaptability could be enhanced for diverse modeling scenarios requiring nuanced control over optimization processes through well-defined boundaries influenced by contextual factors unique to each problem domain.