Related papers: A statistical view on exchanges in Quickselect
We study the almost surely finite random variable $S$ defined by the distributional fixed-point equation \[ S \stackrel{d}{=} 1 + \max\{US', (1-U)S''\}, \qquad U \sim \mathrm{Unif}(0,1), \] where $S'$ and $S''$ are independent copies of…
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous,…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…
Mining frequent itemsets and association rules is an essential task within data mining and data analysis. In this paper, we introduce PrefRec, a recursive algorithm for finding frequent itemsets and association rules. Its main advantage is…
Lecture notes for the Yale Computer Science course CPSC 4690/5690 Randomized Algorithms. Suitable for use as a supplementary text for an introductory graduate or advanced undergraduate course on randomized algorithms. Discusses tools from…
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…
The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is completely unknown. A window-limited leave-one-out…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be…
We prove limit laws for the number of occurrences of a pattern on the fringe of a ranked tree-child network which is picked uniformly at random. Our results extend the limit law for cherries proved by Bienvenu et al. (2022). For patterns of…
We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…
Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…
This paper analyzes single-item continuous-review inventory models with random supplies in which the inventory dynamic between orders is described by a diffusion process, and a long-term average cost criterion is used to evaluate decisions.…
We introduce and study the r-Lah distribution whose definition involves r-Stirling numbers of both kinds. We compute its expectation and variance, show its log-concavity and prove limit theorems for this distribution. We use these results…
Feature selection can facilitate the learning of mixtures of discrete random variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all workers are equally reliable but, if the less reliable ones could be eliminated, then…
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…