What is the difference between Variational Inference (VI) and Markov Chain Monte Carlo (MCMC) for Bayesian posterior inference?

Question

Machine Learning — Hard

What is the difference between Variational Inference (VI) and Markov Chain Monte Carlo (MCMC) for Bayesian posterior inference?

Accepted Answer

MCMC samples from the true posterior but is slow; VI approximates with a tractable distribution. VI sacrifices exactness for speed and scalability, making it more efficient for large datasets.