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Tagged with dirichlet-distribution gamma-distribution
9
questions
1
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1
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126
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Distribution of the ratio of Dirichlet/Gamma variates
It can be seen that the following random variates have the same distribution:
$\frac{X_1 + X_3}{X_2 + X_3}$, where $(X_1, X_2, X_3) \sim \text{Dirichlet} (\alpha_1, \alpha_2, \alpha_3)$
$\frac{Y_1 + ...
0
votes
1
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103
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Combining Dirichlet and Gamma-Normal distributions
I have a model that describes 2 dimensional data where each data points is define as d = [category, x].
The category dimension can take 3 different values with respective probability $p_1$, $p_2$ and $...
- 1
2
votes
1
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Reparameterization trick for the Dirichlet distribution
Summary:
My aim is to create a (probabilistic) neural network for classification that learns the distribution of its class probabilities. The Dirichlet distribution seems to be choice. I am familiar ...
7
votes
1
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Mean of Generalization of the Dirichlet Distribution
I know that if $X_{1},X_{2},...X_{n}$ are independent $\mathrm{Gamma}(\alpha_{i},\theta)$ - distributed variables (notice they all have the same scale parameter $\theta$) and
$Y_{i}=\frac{X_{i}}{\sum_{...
- 101
3
votes
1
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355
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Difficulties in computing the derivatives of the Dirichlet distribution
I need to compute the first derivatives of the Dirichlet distribution, defined in the following way:
$$r(P; \pi, \rho) = \frac{\Gamma(c)}{\prod_{i=1}^{k} \Gamma(c \pi_i)} \cdot \prod_{i=1}^{k} P_i^{c\...
- 57
1
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0
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Utilising the reparameterisation trick on non-Gaussian distributions (Dirichlet)
I'm specifically looking to apply the trick to a Dirichlet distribution. Kingma and Welling (2013) briefly talk about how the trick can be applied to non-Gaussian distributions, and state that the ...
- 175
3
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1
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1k
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Dirichlet sample by normalising Gamma RVs
I know that if you sample $K$ random variables $(X_1, X_2, \dots, X_K)$ from Gamma distributions using shape parameters $(\alpha_1, \alpha_2, \dots \alpha_K)$ and a scale parameter $\theta = 1$ such ...
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28
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Construction of Dirichlet distribution with Gamma distribution
Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
- 2,110
17
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1
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What is the expected value of modified Dirichlet distribution? (integration problem)
It is easy to produce a random variable with Dirichlet distribution using Gamma variables with the same scale parameter. If:
$ X_i \sim \text{Gamma}(\alpha_i, \beta) $
Then:
$ \left(\frac{X_1}{\...
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