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Everything about Variational Bayesian methods

Mathematical methods used in Bayesian inference and machine learning

Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as might be described by a graphical model. As typical in Bayesian inference, the parameters and latent variables are grouped together as "unobserved variables". Variational Bayesian methods are primarily used for two purposes:To provide an analytical approximation to the posterior probability of the unobserved variables, in order to do statistical inference over these variables. To derive a lower bound for the marginal likelihood of the observed data. This is typically used for performing model selection, the general idea being that a higher marginal likelihood for a given model indicates a better fit of the data by that model and hence a greater probability that the model in question was the one that generated the data. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Variational Bayesian methodsA 5-minute orientation
  2. Skim a recent paper: Robust Indoor Localization via Conformal Methods and Variational Bayesian Adaptive FilteringInfluential work since 2022
  3. Pick up a classic book: A modern theory of random variationThe most-reprinted book on the subject
  4. Read the landmark paper: Bayesian parameter estimation via variational methodsCited 416 times
  5. Go sideways: Normal-gamma distributionA closely related topic
  6. Go sideways: Exponential distributionA closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. Mathematical derivation
  2. Mean field approximation
  3. A duality formula for variational inference
  4. A basic example
  5. Further discussion
  6. A more complex example
  7. Exponential-family distributions

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics