Variational Inference¶
Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational Inference: A Review for Statisticians. JASA, 112(518), 859-877.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Approximation
- Statistics and machine learning lean on variational approximations, as Blei et al. (2017) review
This sourceModern review of variational approximation in ML/statistics.
SupportedVerified against the work's full text
A review for statisticians of variational inference, presented as a machine-learning method widely used to approximate Bayesian posterior densities.
“In this paper, we review variational inference (VI), a method from machine learning for approximating probability densities”
- Statistics and machine learning lean on variational approximations, as Blei et al. (2017) review
Domain-specific¶
- Bayes Factor
- . Genetics and bioinformatics — it ranks competing causal models for variant–trait associations across the genome. Machine learning — marginal-likelihood model selection is the same object, with the variational evidence lower bound an explicit surrogate for it
This sourceDerives the evidence lower bound as a bound on the log marginal likelihood and discusses its use as a model-selection surrogate -- while noting that selecting on a bound is not theoretically justified.
Supported in partVerified against the source
- . Genetics and bioinformatics — it ranks competing causal models for variant–trait associations across the genome. Machine learning — marginal-likelihood model selection is the same object, with the variational evidence lower bound an explicit surrogate for it
- Variational Bayesian Methods
- Variational Message Passing
- - If every updated (q_i) is replaced by its exact mean-field coordinate optimum while the other factors are fixed, the ELBO cannot decrease at that step
This sourceSection 2.4 of the review gives this update - each factor set proportional to the exponentiated expected log complete conditional, the others held fixed - and states that coordinate ascent climbs the ELBO monotonically to a local optimum.
SupportedVerified against the source
- - If every updated (q_i) is replaced by its exact mean-field coordinate optimum while the other factors are fixed, the ELBO cannot decrease at that step
Mechanisms¶
- Variational Inference Objective
- Minimizing reverse-KL is mode-seeking and under-estimates the target's spread, so the approximate posterior looks tighter than the truth — dangerous precisely when you are relying on it for uncertainty.
This sourceNotes that KL(q||p)-based variational inference generally underestimates posterior variance, yielding an approximation with tighter spread than the target.
- Minimizing reverse-KL is mode-seeking and under-estimates the target's spread, so the approximate posterior looks tighter than the truth — dangerous precisely when you are relying on it for uncertainty.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 3 of 5 citations: 2 supported, 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:5959ff52faac · see in the full table