Related papers: Approximate Majorization
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
Two approximations are frequently used in statistical physics: the first one, which we shall name the mean values approximation, is generally (and improperly) named as "maximum term approximation". The second is the "Stirling…
Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…
Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply…
The greatest root distribution occurs everywhere in classical multivariate analysis, but even under the null hypothesis the exact distribution has required extensive tables or special purpose software. We describe a simple approximation,…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In this paper, we consider a generalized notion of majorization…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
Finite precision approximations of discrete probability distributions are considered, applicable for distribution synthesis, e.g., probabilistic shaping. Two algorithms are presented that find the optimal $M$-type approximation $Q$ of a…
This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…