Questions tagged [infinite-mixture-model]

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Approximaion with uniform mixture density

Assume that a RV is drawn from a distribution with PDF $f(x)$. I would like to approximate this distribution as a mixture of infinitely many uniform distributions. Without loss of generality, assume ...
Ali Furkan's user avatar
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Is every Compound Poisson distribution a Mixture model?

We have two models: Let $N \sim \hbox Poisson (\lambda)$ and let $(X_k ; k =1,2,3,...)$ be a a sequence of independent and identically distributed random objects (random variables, vectors or ...
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An estimation problem related to a certain stochastic process (radom sum of stochastic processes)

Let $N\sim \hbox{Poisson}(\lambda)$ and $(X_t)_{t \in \mathbb Z}$ be a stochastic process. Consider the following stochastic process: $$ Y_t = \sum_{j=1}^N X_{t,j}$$ where $(X_{t,1})_{t\in \mathbb Z}, ...
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High dimensional behavior of Dirichlet Process-based clustering?

I have a problem stemming from Dirichlet Process Gaussian Mixture Models (DP-GMMs) in high dimension. I'll write this question so that no knowledge of DP-GMMs is needed. Let $D$ be the dimensionality ...
Rylan Schaeffer's user avatar
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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. ...
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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 ...
nikarj's user avatar
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3 votes
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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 ...
calveeen's user avatar
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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 ...
Ivan's user avatar
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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 ...
Mooks's user avatar
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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 ...
MJon10's user avatar
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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 ...
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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 $\beta$ ...
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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^{...
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3 votes
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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 ...
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