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We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…

We consider a type of random processes which satisfies the conditional increment condition and obtain an estimate for the tail probability and a Doob-type inequality of the maximum of the process. The main result is that, for processes…

We study an equivalence of (i) deterministic pathwise statements appearing in the online learning literature (termed \emph{regret bounds}), (ii) high-probability tail bounds for the supremum of a collection of martingales (of a specific…

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle…

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…

We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice…

Let $X$ be the constrained random walk on $\mathbb{Z}_+^d$ $d >2$, having increments $e_1$, $-e_i+e_{i+1}$ $i=1,2,3,...,d-1$ and $-e_d$ with probabilities $\lambda$, $\mu_1$, $\mu_2$,...,$\mu_d$, where $\{e_1,e_2,..,e_d\}$ are the standard…

We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…

We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…

Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood. While…

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

Fix a sequence c=(c_1,...,c_n) of non-negative integers with sum n-1. We say a rooted tree T has child sequence c if it is possible to order the nodes of T as v_1,...,v_n so that for each 1 <= i <= n, v_i has exactly c_i children. Let T be…

Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. For the problem of using network supercomputing to perform a large…