Questions tagged [dirichlet-distribution]
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
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What exactly is the alpha in the Dirichlet distribution?
I'm fairly new to Bayesian statistics and I came across a corrected correlation measure, SparCC, that uses the Dirichlet process in the backend of it's algorithm. I have been trying to go through the ...
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Why is the Dirichlet distribution the prior for the multinomial distribution?
In LDA topic model algorithm, I saw this assumption. But I don't know why chose Dirichlet distribution? I don't know if we can use Uniform distribution over Multinomial as a pair?
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Drawing from Dirichlet distribution
Let's say we have a Dirichlet distribution with $K$-dimensional vector parameter $\vec\alpha = [\alpha_1, \alpha_2,...,\alpha_K]$. How can I draw a sample (a $K$-dimensional vector) from this ...
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Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)?
So this question is slightly messy, but I'll include colourful graphs to make up for that! First the Background then the Question(s).
Background
Say you have a $n$-dimensional multinomial ...
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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 $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
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Distribution of the largest fragment of a broken stick (spacings)
Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment?
More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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Purpose of Dirichlet noise in the AlphaZero paper
In DeepMind's AlphaGo Zero and AlphaZero papers, they describe adding Dirichlet noise to the prior probabilities of actions from the root node (board state) in Monte Carlo Tree Search:
Additional ...
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The input parameters for using latent Dirichlet allocation
When using topic modeling (Latent Dirichlet Allocation), the number of topics is an input parameter that the user need to specify.
Looks to me that we should also provide a collection of candidate ...
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Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters
I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta.
Then, I assume the parameter ...
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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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Why does nobody use the Bayesian multinomial Naive Bayes classifier?
So in (unsupervised) text modeling, Latent Dirichlet Allocation (LDA) is a Bayesian version of Probabilistic Latent Semantic Analysis (PLSA). Essentially, LDA = PLSA + Dirichlet prior over its ...
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Laplace smoothing and Dirichlet prior
On the wikipedia article of Laplace smoothing (or additive smoothing), it is said that from a Bayesian point of view,
this corresponds to the expected value of the posterior distribution, using a ...
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The meaning of representing the simplex as a triangle surface in Dirichlet distribution?
I'm reading from a book that introduces the Dirchilet distribution and then presented figures about it. But I was not really able to understand those figures. I attached the figure here at the bottom. ...
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Is sparsity of topics a necessary condition for latent Dirichlet allocation (LDA) to work
I have been playing with the hyper-parameters of the latent Dirichlet allocation (LDA) model and am wondering how sparsity of topic priors play a role in inference.
I have not performed these ...
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Dirichlet posterior
I have a question about the Dirichlet posterior distribution. Given a multinomial likelihood function it's known that the posterior is $Dir({\alpha_i + N_i})$, where $N_i$ is the number of times we've ...
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