Advances in Variational Inference (1711.05597v3)

Abstract: Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully used in various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

• The paper’s main contribution is a comprehensive review of scalable, generic, accurate, and amortized variational inference methods in Bayesian modeling.
• It highlights novel methodologies such as stochastic optimization, black-box techniques, and alternative divergence measures to enhance flexibility and efficiency.
• The findings underscore that these advances improve VI's capability to process large datasets and complex models across various domains.

Advances in Variational Inference

The paper "Advances in Variational Inference" by Zhang et al. provides a comprehensive review of recent developments in the field of variational inference (VI). Focused on the context of Bayesian probabilistic models, this work explores the significance of VI as a scalable method for approximating complex posterior distributions.

Overview

Variational inference is pivotal in approximating high-dimensional Bayesian posteriors with simpler distributions by optimizing the Kullback-Leibler (KL) divergence. The paper divides recent advances into four key aspects: scalable VI, generic VI, accurate VI, and amortized VI. Each of these areas addresses specific challenges and extends the applicability of VI to broader model classes and larger datasets.

Key Advances

1. Scalable VI: The authors highlight the emergence of stochastic variational inference (SVI), which leverages stochastic optimization techniques to handle large datasets. SVI introduces stochastic approximations that significantly reduce computational costs, while maintaining convergence properties through methods like natural gradients. These advancements enable VI to process data-intensive applications efficiently.
2. Generic VI: Generic VI enhances the flexibility of VI by extending its applicability to non-conjugate models. The paper discusses black box variational inference (BBVI) methods that employ stochastic gradient estimators, such as REINFORCE and reparameterization gradients, to eliminate the need for analytical ELBO derivations. This broadens the range of models that can be effectively addressed using VI.
3. Accurate VI: VI's accuracy has been improved by exploring alternative divergence measures beyond KL, such as $\alpha$-divergences and Stein discrepancies. These measures address issues of underestimating posterior variances and capture more intricate interdependencies within model parameters. Structured variational approximations, like hierarchical variational models, enhance VI's ability to account for complex dependencies in latent variables.
4. Amortized VI: Amortized inference significantly speeds up VI by using inference networks to predict local variational distributions. This advancement is particularly impactful in deep learning architectures, such as variational autoencoders (VAEs), where it allows rapid inference over complex models. VAEs utilize neural networks to approximate posteriors, merging probabilistic modeling with deep learning.

Implications and Future Directions

The reviewed advancements fortify VI as a versatile tool capable of handling large-scale data and complex models. The integration of stochastic optimization, coupled with flexible modeling approaches, democratizes access to Bayesian inference across various domains, including computer vision and healthcare.

Future research may focus on further reducing variational approximations' bias and exploring new divergence measures that better capture model uncertainty. Additionally, increasing the automation of VI through probabilistic programming could substantially streamline its application for broader research communities.

Overall, this paper underscores the ongoing evolution of VI, emphasizing its critical role in unlocking scalable and flexible Bayesian inference methods. The insights offered pave the way for continual breakthroughs in machine learning and AI, steering toward more comprehensive, interpretable, and efficient inference paradigms.