What does variational mean in variational inference?

1 Answer. 1. 12. It means using variational inference (at least for the first two). In short, it’s an method to approximate maximum likelihood when the probability density is complicated (and thus MLE is hard).

What is stochastic variational inference?

2. Stochastic Variational Inference. We derive stochastic variational inference, a stochastic optimization algorithm for mean-field vari- ational inference. Our algorithm approximates the posterior distribution of a probabilistic model with hidden variables, and can handle massive data sets of observations.

Why do variational inferences occur?

The main idea of variational methods is to cast inference as an optimization problem. Suppose we are given an intractable probability distribution p . Variational techniques will try to solve an optimization problem over a class of tractable distributions Q in order to find a q∈Q q ∈ Q that is most similar to p .

How is variational inference ( VI ) used in statistics?

In statistics, variational inference (VI) is a technique to approximate complex distributions. The idea is to set a parametrised family of distribution (for example the family of Gaussians, whose parameters are the mean and the covariance) and to look for the best approximation of our target distribution among this family.

What’s the difference between sampling and variational inference?

The main differences between sampling and variational techniques are that: Unlike sampling-based methods, variational approaches will almost never find the globally optimal solution. However, we will always know if they have converged. In some cases, we will even have bounds on their accuracy.

Which is the procedure for coordinate ascent variational inference?

Such a procedure is known as Coordinate Ascent Variational Inference (CAVI). Further, note that which allows us to write the updates in terms of the conditional posterior distribution of zj given all other factors z−j. This looks a lot like Gibbs sampling, which we discussed in detail in a previous blog post.

How to use variational and exact inference in R?

We derive the variational objective function, implement coordinate ascent mean-field variational inference for a simple linear regression example in R, and compare our results to results obtained via variational and exact inference using Stan. Sounds like word salad? Then let’s start unpacking!