Bayesian Non-Finite Mixture Models
Motivation
Following up from our previous post on Bayesian Finite Mixture Models, here are my notes on Non-Finite mixture model.
Non-finite Mixture Models
Bayesian finite mixture models can be used when we have a prior knowledge or some good guess on the number of groups present in the dataset. But if we do not know this beforehand, then we can use Non-Finite mixture models. Bayesian solution for this kind of problems is related to Dirichlet process.
Dirichlet Process(DP)
We briefly mentioned about Dirichlet distribution in the previous post Bayesian Finite Mixture Models,
which is a generalization of beta distribution, similarly Dirichlet Process is an infinite-dimensional generalization of Dirichlet
distribution. The Dirichlet distribution is a probability distribution on the space of probabilities, while Dirichlet Process
is a probability distribution on the space of distributions. A Dirichlet Process is a distribution over distributions.
When I first read this, my mind went
.
What this means is, that a single draw from a Dirichlet distribution will give us a probability and a single draw from a Dirichlet Process will give us a Dirichlet distribution. For finite mixture models, we used Dirichlet distribution to assign a prior for the fixed number of clusters, Continue reading

