Related papers: Optimal Upper and Lower Bounds for Boolean Express…
This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…