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Also known as: Variational Bayes, Approximate inference
An optimization-based approach that approximates complex posterior distributions with tractable families by maximizing the ELBO.
DESCRIPTION
Variational inference replaces exact Bayesian inference with optimization, selecting parameters of an approximate distribution to minimize divergence to the true posterior. Common strategies include mean-field factorization and coordinate ascent, while stochastic VI scales to large datasets. Amortized VI, used in VAEs, leverages neural networks to parameterize posteriors. VI is faster than many MCMC methods but can introduce approximation bias.
ALTERNATIVE DEFINITIONS
Blei, Kucukelbir, McAuliffe (Variational Inference: A Review for Statisticians)
Variational inference converts inference into optimization.
Concise characterization framing VI as an optimization problem.
Wikipedia
In statistics, variational Bayesian methods are a family of techniques for approximating posterior distributions and related quantities in Bayesian inference.
Defines VI within the Bayesian inference context.
Pyro
Variational inference uses optimization to fit an approximate posterior.
Developer-focused explanation of VI as posterior fitting.
RELATED TERMS
Bayesian Inference Evidence Lower Bound Mean-Field Approximation Variational Autoencoder KL Divergence Amortized Inference Stochastic Variational Inference Coordinate Ascent Posterior
COMPETING TERMS
Markov Chain Monte Carlo
RELATIONS
- Broader: Inference
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer MLOps Engineer
EXTERNAL SOURCES
- Wikipedia - Variational Bayesian methods
- Blei et al. - Comprehensive VI review
- Pyro - Intro to VI with code
- TensorFlow Probability - VI examples with TFP
TOP QUESTIONS
What is Variational Inference?
It approximates intractable posteriors by optimizing parameters of a tractable family to maximize the ELBO.
Category: Definition
Why use Variational Inference instead of MCMC?
VI scales better and is faster for large datasets, though it introduces approximation bias compared to sampling-based methods.
Category: Opinion
What is the ELBO in Variational Inference?
The Evidence Lower Bound is the objective optimized to fit the approximate posterior to the true posterior.
Category: Definition
What does mean-field Variational Inference assume?
It factorizes the approximate posterior into independent components, simplifying optimization at the cost of expressiveness.
Category: Requirements
What is amortized Variational Inference?
It uses neural networks to predict posterior parameters for data points, as in variational autoencoders.
Category: Example
What are common mistakes with Variational Inference?
Choosing an overly restrictive family, poor initialization, and ignoring diagnostics can lead to biased estimates.
Category: Mistakes
What is a competing approach to Variational Inference?
Markov Chain Monte Carlo provides asymptotically exact samples but may be computationally expensive.
Category: Alternatives
What is currently a hot topic around Variational Inference?
Normalizing flows, black-box VI, and variational objectives beyond KL are active research areas.
Category: Topic
How do I apply Variational Inference in practice?
Select an approximate family, derive or use automatic gradients for the ELBO, and validate with posterior predictive checks.
Category: HowTo
Where should I start learning about Variational Inference?
Read Blei’s review and experiment with Pyro or TensorFlow Probability tutorials to build intuition.
Category: Resources