All Questions
Tagged with dirichlet-distribution dirichlet-process
33
questions
4
votes
2
answers
645
views
Dirichlet distribution with correlated components?
I am working with models that use Dirichlet distributions. However, I want to account for correlations between components. If this question is a duplicate, I'd also appreciate any pointers to the ...
1
vote
0
answers
139
views
Stick-breaking construction of Dirichlet distribution vs Dirichlet process
Let $F_0$ be some probability measure and $\alpha > 0$ be the concentration parameter. I can draw a random distribution from $F\sim \mathrm{DP}(\alpha, F_0)$ using the stick-breaking construction:
\...
- 183
1
vote
0
answers
66
views
Dirichlet Process posterior with partially observed data
Suppose I dipose of a set of independant observed couples $(x_1,y_1),...,(x_N, y_N)$ from a joint distribution $P(x,y)$. Furthermore, I suppose that the random distribution $P$ as a Dirichlet prior
$P\...
- 11
2
votes
1
answer
71
views
Let $H$ be the base distribution of a Dirichlet process. How is this process well-defined in case $H(B_1) = 0$?
I have read that the parameters of Dirichlet distribution must be strictly positive.
The Dirichlet distribution of order $K \geq 2$ with parameters $\alpha_{1}, \ldots, \alpha_{K} \color{blue}{> 0}...
- 433
0
votes
0
answers
95
views
Mixtures of Dirichlet multivariates or Dirichlet processes
I am exploring the properties of Dirichlet distributions and their parameters. When mixing two Dirichlet distributed random bivariates
$$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$
...
3
votes
0
answers
131
views
A clarification in the original Dirichlet Process paper by Ferguson
I am reading the paper "Bayesian Analysis of Some Nonparametric Problems" by Ferguson where the Dirichlet process is introduced. There is a proposition 5 where the joint distribution of ...
- 1,572
1
vote
0
answers
47
views
Marginal Cluster assignments for Dirichlet Process mixture model
I am watching Tamara' Broderick video on Dirichlet Process mixture models where she talks about computing $p(z_n = k | z_1,z_2,..z_{n-1})$ at ardoun 16:06. The z's are drawn from $$\rho_1 \sim beta(...
- 1,116
0
votes
2
answers
342
views
Fitting/Inference for Dirichlet Process/CRP for clustering
Please excuse my ignorance on this topic, I don't have much experience in nonparametric Bayes. I read about Dirichlet process clustering and the Chinese Restaurant Process analogies. I think I ...
1
vote
1
answer
255
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 ...
- 13
2
votes
1
answer
289
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 ...
- 545
0
votes
2
answers
2k
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 ...
- 149
1
vote
0
answers
357
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 ...
- 171
3
votes
1
answer
343
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 ...
- 145
3
votes
1
answer
220
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 ...
- 2,053
1
vote
0
answers
226
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 ...
- 11