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Questions tagged [dirichlet-process]

A family of stochastic processes whose realizations are probability distributions

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Dirichlet Process Concentration Parameter - collapse at zero

Background I've implemented the blocked gibbs sampler for sampling from the posterior of a dirichlet process mixture model as described on p.552 of Bayesian Data Analysis, placing a Gamma prior on the ...
43 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 ...
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Definition of the dirichlet process: what is the sequence of random variables

Reference material by Dr. Teh Definition Given a measureable set S, a base probability distribution H and a positive real number $\alpha$, the Dirichlet process $DP(H, \alpha)$ is a stochastic ...
42 views

Clusters keep switching in Gibbs sampling of Dirichlet Process Mixture Model

All the code and data for this question is on GitHub (stackexchange.R script). I've got multivariate Bernoulli data that I'd like to analyse using Bayesian Mixture ...
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234 views

Coding a simple Stick-Breaking Process in Python

I've just red the great 2012 blog post of Edwin Chen about Dirichlet Process with companion code in R and Ruby. Then I'm trying to translate the Stick-Breaking Process from R to Python. I've got this ...
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Relation between Chinese restaurant process (CRP) vs Dirichlet Process (DP)

There are multiple questions regarding the topic and but I have not found an answer to my doubts. Particularly: On Wikipedia Dirichlet Process page, regarding the connection between the Chinese ...
118 views

Gibbs sampler for Dirichlet Process concentration parameter

I am trying to implement a Gibbs sampler for Hierarchical Dirichlet process, but I cannot seem to correctly estimate the concentration parameters. I therefore started testing just this part of a ...
44 views

HDP: Gibbs sampler implementation

I am trying to recreate the model proposed by Gao et al. (2011), based on the Hierarchical Dirichlet Process proposed by Teh and al. (2005). To estimate the model (let's call it iHDP) I need to ...
83 views

Dirichlet-Multinomial Distribution with many zero counts

Short version: Is there someway to make the dirchlet-multinomial distribution sensitive to the presence of zero counts? Long version: I am attempting model metric positions in musical data. You can ...
54 views

How to interpret graphical model for Dirichlet process mixture for variational inference?

I am working through this paper by Blei and Jordan, which introduces variational inference for Dirichlet process mixtures. They derive an evidence lower bound (ELBO) function based on a stick breaking ...
56 views

How to actually draw a distribution from a given Dirichlet process?

I am wondering if there's an algorithm to actually draw a distribution from a given Dirichlet process. The closest thing I've came across is the stick-breaking construction of a Dirichlet process, but ...
123 views

Understanding Dirichlet Process Mixtures

I have been reading a ton of stuff online and have a question about my understanding of Dirichlet Process Mixtures. First some basics on what I understand: Dirichlet Distribution: multivariate ...
86 views

Explanation of Formal Definition of Dirichlet Process

I am reading about the Dirichlet process and I can understand the construction from Chinese restaurant process or stick-breaking process or Polya urn scheme. Now I am trying to understand why ...
261 views

Stick-breaking construction of Dirichlet process

In the stick-breaking construction of Dirichlet (let me base things on Sethuraman's construction - slide 6 of this) do we sample one $\phi$ vector from the base distribution $H$ and use it for ...
79 views

Why is the Dirichlet Process not a completely random measure?

A completely random measure assigns independent mass to nonintersecting subsets. I cannot figure, however, how the Dirichlet Process does not qualify as a CRM? Aren't the atoms all independent from ...
89 views

Dirichlet process and clustering

How does clustering with a Dirichlet process as prior work? I am confused as to if the parameter $\alpha_i$ $\sim$ DP is found via clustering or is used to cluster. I undestrand how it can be used to ...
45 views

Clustering and Dirichlet process' parameter

I am reading a paper in which they describe a bayesian model in which the prior $a_i$ is defined as a Dirichlet Process (DP). They say: "We use a DP to find the optimal $a_i$ via clustering". Later on ...
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Q about closed form of distribution

Suppose you have a K boxes, each with associated probability $p_i$. You start putting balls in the boxes with probability of putting a ball in a box being proportional to $(n_i+1)\cdot p_i$ where $n_i$...
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Applications of Hierarchical Dirichlet Process to Continuous Data

I read Yee Whye Teh et al.'s paper on Hierarchical Dirichlet Process. In section 5, they show sampling algorithm using base distribution H and data distribution F. One of their applications is HDP-...
403 views

Predictive Density for Dirichlet Multinomial

I am wondering what the predictive distribution of a Dirichlet-Multinomial distribution is. In this tutorial (page 24), the predictive density is simple and something like "pseudo samples." However, ...
233 views

Collapsed Gibbs sampler on Hierarchical Dirichlet Process Mixture Model

I am trying to design a collapsed Gibbs sampler on a mixture model based on Hierarchical Dirichlet Process ($g\sim DP(\gamma, b)$, $\pi\sim DP(\alpha, g)$ ). Should I resample from the posterior of ...
180 views

In a Dirichlet process, can the base distribution be discrete?

Must it be continuous? Note we are talking about the base distribution. The sampled distribution is discrete. 1) If the base distribution is continuous, drawing from it will get a new value (a new ...
38 views

functionals of Dirichlet process mixture

I want to solve (or simulate) /int f(x)G(dx) where f is a function(or phrase of x) and G is DPM(Dirichlet Process mixture prior). Muliere (1998) approximate this ...
535 views

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Bayesian nonparametrics vs model selection using Minimum Message Length

As we know mixture models are important tools in density estimation and in general in statistical machine learning. I have always used nonparametric Bayesian mixture models to avoid the problem of ...
156 views

Notation for base distribution in Dirichlet process

I have a (hopefully simple) question about notation when defining a DP. I have read a lot of papers on DPs, but this is not clear to me, or at least I have not noticed a convention. Say that I am ...
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Gibbs sampling with constraints

I am reading tutorials on Gibbs sampling for partition sampling in Dirichlet Process (Chinese Restaurant Process), and have been struggling to understand the terminology used in the tutorials. To ...