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Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
We construct a new sufficient conditions for boundedness or continuity of arbitrary random fields relying on the so-called partition scheme, alike in the classical majorizing measure method. We deduce also the used in the practice…
In this paper, we further study the concepts of hop domination and 2-step domination and introduce the concepts of restrained hop domination, total restrained hop domination, 2-step restrained domination, and total 2-step restrained…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
Let $E$ be a bounded open subset of $\mathbb{R}^n$. We study the following questions: For i.i.d. samples $X_1, \dots, X_N$ drawn uniformly from $E$, what is the probability that $\cup_i \mathbf{B}(X_i, \delta)$, the union of $\delta$-balls…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, 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…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
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…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
For probability distributions on $\mathbb{R}^n$, we study the optimal sample size N = N(n,p) that suffices to uniformly approximate the pth moments of all one-dimensional marginals. Under the assumption that the marginals have bounded 4p…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…