Related papers: Tight Probability Bounds with Pairwise Independenc…

Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…

Probabilities of Causation play a fundamental role in decision making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions such as monotonicity. In the absence of such…

Let $\{Z_k\}_{k\geqslant 1}$ denote a sequence of independent Bernoulli random variables defined by ${\mathbb P}(Z_k=1)=1/k=1-{\mathbb P}(Z_k=0)$ $(k\geqslant 1)$ and put $T_n:=\sum_{1\leqslant k\leqslant n}kZ_k$. It is then known that…

Two sequential estimators are proposed for the odds p/(1-p) and log odds log(p/(1-p)) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the…

We investigate variance bounds under symmetry constraints in classical, free, and Boolean probability, focusing on Bernoulli distributions and their noncommutative analogues, projections with trace \(p\). We show that symmetrizers under…

Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…

The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…

The Birkhoff graph $\mathcal{B}_n$ is the Cayley graph of the symmetric group $S_n$, where two permutations are adjacent if they differ by a single cycle. Our main result is a tighter upper bound on the independence number…

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…

Let F:=(f_1,...,f_n) be a random polynomial system with fixed n-tuple of supports. Our main result is an upper bound on the probability that the condition number of f in a region U is larger than 1/epsilon. The bound depends on an integral…

We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…

We show that a coupling of non-colliding simple random walkers on the complete graph on $n$ vertices can include at most $n - \log n$ walkers. This improves the only previously known upper bound of $n-2$ due to Angel, Holroyd, Martin,…

Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation…

We study threshold properties of random constraint satisfaction problems under a probabilistic model due to Molloy. We give a sufficient condition for the existence of a sharp threshold that leads (for boolean constraints) to a necessary…

Let $ V_{n} = X_{1,n} + X_{2,n} + \cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\lambda_{n} = \sum\limits_{i=1}^{n} b(i;n) $, $\lambda = \lim\limits_{n \to \infty}…

We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction…

The evaluation of the probability of union of a large number of independent events requires several combinations involving the factorial and the use of high performance computers with several hours of processing. Bounds and simplifications…

Time-sensitive networks require timely and accurate monitoring of the status of the network. To achieve this, many devices send packets periodically, which are then aggregated and forwarded to the controller. Bounding the aggregate…

Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…