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A fundamental property of codes, the second-order weight distribution, is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles. A series of results, parallel to those for weight…
Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…
Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal…
Projected momentum distributions of electrons, i.e. Compton profiles above the topmost atomic layer have recently become experimentally accessible by kinetic electron emission in grazing-incidence scattering of atoms at atomically flat…
Recent work on weighted model counting has been very successfully applied to the problem of probabilistic inference in Bayesian networks. The probability distribution is encoded into a Boolean normal form and compiled to a target language,…
In the chip-firing variant, Diffusion, chips flow from places of high concentration to places of low concentration (or equivalently, from the rich to the poor). We explore this model on complete graphs, determining the number of different…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
This paper analyzes a class of dissemination algorithms for the discovery of distributed contents in Peer-to-Peer unstructured overlay networks. The algorithms are a mix of protocols employing local knowledge of peers' neighborhood and…
For the selfdecomposable distributions (random variables) we identified background driving probability distributions in their random integral representations. For log-gamma and their background driving random variables series…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…