Related papers: Constrained Quantization for Uniform Distributions…

We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…

The purpose of quantization for a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonuniform probability measure $P$ on $\mathbb R^2$ which has support the Sierpi\'nski…

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…

Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…

We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…

Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists…

This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular $m$-sided polygons inscribed in a circle. The result shows that the quantization…

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…

Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…

We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

The problem of clustering a set of points moving on the line consists of the following: given positive integers n and k, the initial position and the velocity of n points, find an optimal k-clustering of the points. We consider two…

We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…