Related papers: Probabilistic Recurrence Relations for Work and Sp…

We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. Several classical textbook algorithms have quite efficient expected-runtime complexity, whereas…

Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…

Consider $n$ real/complex, independent/dependent random variables with respective tail bounds and $g$ a measurable function of the r.v.'s. Consider $f$ the "sharpest" tail bound of $g$ (sharpest in the sense that if $f$ were any less, then…

In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…

We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability…

We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…

Given a hierarchical plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that its meets a deadline, or, alternately, that its {\em makespan} is less…

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…

This paper addresses the advancement of probability tail bound analysis, a crucial statistical tool for assessing the probability of large deviations of random variables from their expected values. Traditional tail bounds, such as Markov's,…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…

All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…

Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest…