All Questions
Tagged with dirichlet-distribution self-study
18
questions
1
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0
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97
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Advice on how to solve a constrained KL Divergence problem between a Dirichlet and a Logistic Normal
I would like some advice or path to follow to solve the following problem.
Consider a random variable $Y$ that follows a Dirichlet distribution $Y \sim Dir(\alpha)$. Let $X$ be a member of the ...
- 76
2
votes
1
answer
139
views
Upgrading weight parameters to random variable in Gaussian mixtures
In a Gaussian mixture model we model a density like:
$p(\mathbf{x}|\pi,\mu,\sigma)=\sum \pi_i N(\mathbf{x}|\mu_i,\sigma_i)$ [1]
where $\pi,\mu$ and $\sigma$ are parameters.
I would like to know if the ...
- 910
3
votes
0
answers
131
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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
5
votes
1
answer
668
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Deriving the marginal multivariate Dirichlet distribution
I am trying to understand how my professor (see derivation below) has derived the multivariate marginal distribution of a subvector of $\theta_j$´s from a Dirichlet distribution. I understand ...
- 83
0
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0
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27
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Question about possible typo in a tutorial about the stick-breaking model of the Dirichlet distribution
I am reading a tutorial on the Dirichlet distribution: http://mayagupta.org/publications/FrigyikKapilaGuptaIntroToDirichlet.pdf
and I think there is a typo in Step 2 of the stick-breaking model of ...
1
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0
answers
347
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Dirichlet Multinomial Posterior Predictive Distribution for Language Model
I have been trying to teach myself about Bayesian analysis, and whilst I have been through the theory several times, I am struggling to actually apply it. I have found some questions online to ...
- 571
1
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0
answers
685
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Marginal Likelihood of Multinomial Dirichlet model
To find the marginal likelihood of the multinomial Dirichlet model, I tried the following:
$$\int_\theta p(N|\theta)p(\theta)d\theta=\frac{n!}{n_1!...n_K!}\frac{\Gamma(\sum_{k=1}^K\alpha_k)}{\Pi_{k=1}^...
- 153
6
votes
2
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4k
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Find marginal distribution of $K$-variate Dirichlet
I've already seen https://math.stackexchange.com/questions/1064995/marginal-of-dirichlet-distribution-is-beta-integral, but need to extend this to the $K$-variate case.
We have $\mathbf{x} = \begin{...
- 5,077
4
votes
0
answers
114
views
what is this property? $\int p(x,\pi)d\pi=p(x|E[\pi])$?
Sorry if the title does not make sense, from the answer of this question Mistake in derivation about categorical distribution and Dirichlet distribution? it can be shown that
say $p(x|\pi)$ follows ...
- 16.6k
1
vote
1
answer
380
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Mistake in derivation about categorical distribution and Dirichlet distribution?
$p(x|\pi)$ follows the categorical distribution (the multinomial with one observation), where $\sum\pi_i=1$ and $x$ is a one-hot vector, and $p(\pi|\alpha)$ follows the Dirichlet distribution.
$p(x|\...
- 16.6k
5
votes
0
answers
55
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how does the beta function make the total probability of Dirichlet distribution integrate to 1? [duplicate]
the Dirichlet distribution $$Dir(\boldsymbol\mu|\boldsymbol\alpha)=\frac{1}{B(\boldsymbol\alpha)}\prod_K\mu_k^{\alpha_k-1}$$
How is the normalization term $B(\boldsymbol\alpha)$ calculated?
or in ...
- 16.6k
2
votes
1
answer
159
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How to deduct the coefficient of the Dirichlet distribution? [duplicate]
I am studying the textbook Introduction to Probability Models by Sheldon Ross. In Section 3.6 page 151 (10th edition), the author uses the Dirichlet distribution to deduct the coefficient of a "...
- 127
5
votes
2
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669
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Polya Urn - formulas
I am trying to understand Dirichlet processes and Polya's Urn, following this excellent article.
One thing that I am struggling with, is to understand in the example below what why the number of ...
- 2,202
2
votes
1
answer
121
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dirichlet process - formula explanatation
i am self-studying the Dirichlet process, from among others http://www.stat.ubc.ca/~bouchard/courses/stat547-sp2011/notes-part2.pdf, and struggling with the following basic question:
I understand ...
- 2,202
2
votes
0
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161
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Dirichlet predictive distribution
I need to derive a posterior predictive density for observation T+1 given that the posterior distribution of $(x_{1}, x_{2}, 1-x_{1}-x_{2})$ is a Dirichlet distribution with parameter $(\alpha_{1}, \...
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