Questions tagged [discrete-distributions]

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How to solve for the minimum KL Divergence when the distribution is discrete?

Say we have a simple case of $p(x,y)$ is a 3x3 matrix: $$\begin{bmatrix} 1/6 & 0 & 0 \\ 1/6 & 3/6 & 0 \\ 0 & 0 & 1/6 \end{bmatrix}$$ And $q(x,y)=...
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Categorical sampling without instantiating probability vector

I want to sample from a discrete distribution with probability vector $p \in \mathbb R^n$, where $n$ is large. Suppose that $p_i = f_i / Z$, where $Z$ is a normalization constant. I can compute the ...
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The meaning of a parameterization of the logarithmic distribution

In calculus one learns that $$ p + \frac{p^2} 2 + \frac{p^3} 3 + \frac{p^4} 4 + \cdots = -\log(1-p). \tag 1 $$ Thus a discrete probability distribution on the set $\{1,2,3,\ldots\}$ is given by $$ \Pr(...