# Questions tagged [pr.probability]

Questions in probability theory

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### Speed networking algorithm

I have 40 people and 10 tables that can accommodate 4 people at a time. The task is to make sure that every person seats with every other person at the same table exactly once, that is every person ...
1 vote
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### Optimization: Turning a sparse graph of probabilities into the maximum likelihood DAG

I have a sparse matrix of probabilities that I want to turn into a DAG. If x[m,n] = pr it means that m is a descendent (direct or transitively) of n with probability pr. I want to construct a DAG over ...
168 views

### An additive combinatoric probability question

Let $A,B \subset [d]$, where $[d] = \{0,...,d \}$, such that $A\cap B = \phi$ and $|A| = |B| = \frac{d+1}{2}$. I was studying the size of $|(2A \cup 2B) \triangle (A+B)|$, where $\triangle$ is the ...
53 views

### Non regular distribution in [0,1] examples

We say a distribution is regular is its associated virtual function \psi(x) = x - (1-F(x))/f(x) is monotone non decreasing. Here F and f are CDF and PDF for the distribution. How do I construct an ...
51 views

### Is there any bound on the convergence rate of actions in bandit literature?

In classical bandit problems where there are $K$ arms and we should decide which arm to pull at each period, the main issue is to design an algorithm that minimizes the regret and we find a bound on ...
41 views

### Proof that Sufficiency and Caliberation by group are equivalent notions

I am currently reading through the Fairness and Machine Learning book and I have a problem understanding the proof of Proposition 1 in Chapter 3 (titled Classification) (https://fairmlbook.org/...
280 views

### Chernoff bound for weighted sums of Bernoulli random variables

I tried to prove the following Chernoff-type bound when doing research, and found that it is of indepent interest. Let $X_1, \dots, X_n$ be independent random varibles such that each $X_i$ is a ...
1 vote
81 views

### A bound that follows from submodularity

I am studying Lemma 1 of this paper: The Adaptive Complexity of Maximizing a Submodular Function. The proof appears on page 11. I got stuck on this inequality: where $f$ is a monotone submodular set ...
62 views

### How do I calculate the information content of a mass spectrum?

Ions in a mass spectrum are represented using two independent values for the mass-to-charge ratio [m/z] of the ion and it's relative abundance. Here's an example for caffeine from HMDB: https://hmdb....
1 vote
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### Is there a known notion of "stochastic dependent pair"?

I came upon this when thinking about the semantics of probabilistic programs. Say you have a generative model N ~ Poisson() for n = 1:N X[i] ~ Normal() Then the ...
185 views

### Complexity of finding the most likely edge

Consider a connected, unweighted, undirected graph $G$. Let $m$ be the number of edges and $n$ be the number of nodes. Now consider the following random process. First sample a uniformly random ...