Questions tagged [infinite-mixture-model]
11 questions
8
votes
1 answer
Can a (possibly infinite) mixture of Gaussians be Gaussian?
Suppose we define a (possibly infinite) mixture of zero-mean Gaussians:
$$p(x) = \int_{\mathbb{R}^+} N(x; 0, \sigma^2)\ \pi(\sigma)\,\text d\sigma,$$
where $\pi$ defines the mixture components. Obviously, if $\pi$ is a point mass on some standard…
Allen94
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4
votes
1 answer
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 where $\pi, \Psi, \Sigma, \mu, \boldsymbol{Z}$ are…
calveeen
- 746
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- 10
4
votes
1 answer
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 model. The three steps are as follows:
Update…
Ivan
- 458
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3
votes
1 answer
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 Dirichlet Process Mixture Model (using Gibbs/MCMC)…
ilanman
- 4,503
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2
votes
1 answer
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 distribution, and
$
\mu,\Sigma \sim NIW(\beta)
$
where…
tisPrimeTime
- 380
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2
votes
0 answers
Any connections between mixed model and mixture of experts model?
Given data $$ for $i \in \{1, 2, 3, \dots n\}$ ($n$ samples), and we are interested in knowning the relationship between $y$ and $X$. In the simplest manner, we can solve for $\beta$ where:
$$
y = X\beta + \epsilon
$$
Soving $\beta$ by…
user42004
2
votes
0 answers
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:
$f(x) = \sum_1^{\infty} p_i h(x|\mu_i,\sigma_i)$
with…
user166243
1
vote
1 answer
Validity of BIC for Dirichlet process mixture models
I am implementing clustering using Dirichlet process mixture models via scikit learn's Variational Bayesian Gaussian Mixture model. I arrived at the appropriate priors iteratively, and I am able to plot the graph of inferred cluster count to prior…
nikarj
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- 3
1
vote
0 answers
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 applies to my real world problem.
I am measuring…
Mooks
- 686
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1
vote
1 answer
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 points that are assigned to cluster j, where…
MJon10
- 13
- 3
0
votes
0 answers
normal mean variance mixture garch with OBSERVED mixing variable
I need to estimate this univariate garch model with the following discription
My model (regression):
Yt=mu + gamma * Gt + et
Gt is GIVEN
Where the crucial part is that:
et= sqrt(Gt) * sqrt(ht) * Zt
where:
zt∼N(0,1)
Variance equation:
ht=omiga +…
Ananas
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