Contents
How does variational Bayes solve the Bayesian inference problem?
To summarize, variational Bayes has these ideas: The Bayesian inference problem of finding a posterior on the unknown variables (parameters and latent variables) is hard and usually can’t be solved analytically. Variational Bayes solves this problem by finding a distribution Q that approximates the true posterior P.
Which is the core strategy of variational inference?
This is the core strategy of variational inference. In variational Inference we use the maximization of the ELBO as a proxy for minimization of the KL divergence. This in turn optimizes our approximation of the true posterior by the approximate posterior.
How is the mean field approximation used in Bayes?
The mean-field approximation partitions the unknown variables and assumes each partition is independent (a simplifying assumption). With some (long) derivations, we can find an algorithm that iteratively computes the Q distributions for a given partition by using the previous values of all the other partitions.
How is the Elbo used in variational inference?
In variational Inference we use the maximization of the ELBO as a proxy for minimization of the KL divergence. This in turn optimizes our approximation of the true posterior by the approximate posterior. In the following tutorial, we will derive each of the above equations in clear stepwise detail.
How to model an univariate Gaussian with unknown mean and variance?
Fitting a univariate Gaussian with unknown mean and variance : Given observed data X = {x1, …, xN}, we wish to model this data as a normal distribution with parameters μ, σ2 with a normally distributed prior on the mean and an inverse-gamma distributed prior on the variance. More precisely, our model can be defined as:
How to describe a Bayesian Gaussian mixture model?
Bayesian Gaussian Mixture Model : A Bayesian Gaussian mixture model with K mixture components and N observations {x1, …, xN}, latent categorical variables {z1, …, zN}, parameters μi, Λi, π and hyperparameters μ0, β0, ν0, W0, α0, can be described as such: