What is the meaning of mean field?
In physics and probability theory, mean field theory (MFT) or self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic …
What is the mean field approximation as used by variational inference?
In the mean-field approximation (a common type of variational Bayes), we assume that the unknown variables can be partitioned so that each partition is independent of the others. Using KL divergence, we can derive mutually dependent equations (one for each partition) that define the shape of Q.
Why is it called variational inference?
The term variational is used because you pick the best q in Q — the term derives from the “calculus of variations,” which deals with optimization problems that pick the best function (in this case, a distribution q).
What is mean field approach?
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters.
Why do we need variational inference?
Variational Bayesian methods are primarily used for two purposes: To provide an analytical approximation to the posterior probability of the unobserved variables, in order to do statistical inference over these variables.
Is variational inference Bayesian?
One such approximate inference technique that has gained popularity in recent times is the Variational Bayes (VB). Having a relatively low computational cost and a good empirical approximation has propelled it to drive the intuition behind successful models like the Variational Auto-encoders and more.
What does variational mean in machine learning?
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 do you mean by field theory in mathematics?
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
Is variational inference exact?
Since variational inference is formulated as an optimization problem, we do have certain indications on the progress. However, variational inference approximates the solution rather than finding the exact solution. Indeed, it is unlikely that our solution will be exact.