What is meant by mean-field approximation?

The mean field approximation is a technique that can be used to calculate approximate partition functions for systems composed of interacting particles. The problem with calculating such partition functions exactly comes when one attempts to enumerate all the possible microstates and calculate their energy.

What is the meaning of mean field?

In physics and probability theory, mean-field theory (aka MFT or rarely 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 …

What means field potential?

The mean field potential is considered such that the stationary Schrödinger equation is solved simply to obtain single particle states and their related energy spectrum. These single-particle states are used to construct the N particle wave function as follows.

What is mean field distribution?

Loosely speaking, the mean field family defines a specific class of joint distributions. So z here is actually a parameter vector of length m. That means that q(z) describes a joint distribution over all of the individual z’s, and can be written as. q(z)=q(z1,z2,…, zm)

What is mean field assumption?

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. The mean-field approximation partitions the unknown variables and assumes each partition is independent (a simplifying assumption).

What does ELBO mean?

In statistics, the evidence lower bound (ELBO, also variational lower bound or negative variational free energy) is a quantity which is often optimized in Variational Bayesian methods.

What is ELBO VAE?

Variational Autoencoder (VAE): in neural net language, a VAE consists of an encoder, a decoder, and a loss function. Training means minimizing these loss functions. But in variational inference, we maximize the ELBO (which is not a loss function). This leads to awkwardness like calling optimizer.

What is the mean-field assumption?

What is meant by mean-field approximation? The mean field approximation is a technique that can be used to calculate approximate partition functions for systems composed of interacting particles. The problem with calculating such partition functions exactly comes when one attempts to enumerate all the possible microstates and calculate their energy. What is the meaning of…