Questions tagged [infinite-mixture-model]

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Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
3
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0answers
48 views

Implementation of a blocked Gibbs sampler for a mixture model with a Dirichlet-process prior

I am trying to understand and implement the blocked Gibbs sampler described on page 552 in Bayesian Data Analysis by Gelman et al. in the context of using a Dirichlet process as a prior in a mixture ...
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31 views

Mixture or Convolution

tl;dr is final paragraph at the bottom. I have read the posts explaining the differences between mixture distributions and convolutions of distributions, but am having a hard time understanding which ...
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1answer
62 views

Bayesian Inference: Prior in Chinese Restaurant Process

For the Chinese restaurant process, as used in Dirichlet Process mixture models, we have a prior that data point i belongs to cluster j, where c is an indicator. n represents the total number of data ...
2
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1answer
119 views

Clarifying Dirichlet Process Mixture Probability Terms

Suppose I have a Dirichlet Process Mixture model defined as follows: $\alpha \sim G(a,b)\\ \pi|\alpha \sim \text{Dir}(\alpha)\\ z|\pi \sim \text{Cat}(\pi)\\ $ where $G$ is just a standard Gamma ...
2
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0answers
43 views

Any connections between mixed model and mixture of experts model?

Given data $<y_i, X_i>$ for $i \in \{1, 2, 3, \dots n\}$ ($n$ samples), and we are interested in knowning the relationship between $y$ and $X$. In the simplest manner, we can solve for $\beta$ ...
2
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0answers
34 views

Estimation of arbitrary density on the real line with infinte Gaussian mixtures

In his Introduction to this paper, Ferguson says that we can model an arbitrary density f(x) on the real line as the mixture of a countable number of normal distributions in the form: $f(x) = \sum_1^{...
3
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1answer
301 views

Check on intuition behind infinite mixture models for clustering

I'm trying to better understand the intuition and practical application of infinite mixture models (Dirichlet Process) and finite mixture models. For example, say I have a data set on which I run a ...