Variational Inference¶
Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational Inference: A Review for Statisticians. Journal of the American Statistical Association, 112(518), 859-877.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Approximation
- … algorithms for NP-hard problems, as Vazirani (2001) systematizes (Williamson and Shmoys (2011) method), sketching and sampling algorithms (count-min sketch, HyperLogLog) that trade exactness for sublinear memory. Statistics and machine learning lean on variational approximations, as Blei et al. (2017) review
This sourceModern review of variational approximation in ML/statistics.
- … algorithms for NP-hard problems, as Vazirani (2001) systematizes (Williamson and Shmoys (2011) method), sketching and sampling algorithms (count-min sketch, HyperLogLog) that trade exactness for sublinear memory. 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.
- . 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.
- - 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
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