Variational Inference (VI) is a machine learning method that approximates probability densities through optimization. In the Bayesian context, it approximates the posterior distribution as follows:
- Select a parametrized family of probability distributions
- Find the member of this family closest to the target, as measured by Kullback-Leibler divergence
Compared to MCMC, Variational Bayes tends to converge faster and scales to large data better. While MCMC approximates the posterior with samples from the chain that will eventually converge arbitrarily close to the target, variational algorithms approximate the posterior with the result of the optimization, which is not guaranteed to coincide with the target.
Variational Inference is better suited for large datasets and to quickly explore many models. In contrast, MCMC will deliver more accurate results on smaller datasets or when time and computational resources pose fewer constraints.