Related papers: Gibbs Measures and Phase Transitions on Sparse Ran…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
We consider disordered lattice spin models with finite volume Gibbs measures $\mu_{\L}[\eta](d\s)$. Here $\s$ denotes a lattice spin-variable and $\eta$ a lattice random variable with product distribution $\P$ describing the disorder of the…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
The following is a short report about recent work on discrete physics/mathematics on the Planckscale and the use of the concept of ''random graphs'' in this business, appearing in the group21-proceedings (Gosslar 1996)
We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…
The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods,…
Restricted Boltzmann Machines are a class of undirected graphical models that play a key role in deep learning and unsupervised learning. In this study, we prove a phase transition phenomenon in the mixing time of the Gibbs sampler for a…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher dimensional distributions to those targeting lower dimensional ones. This leads to a quasi-telescoping property of…
Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
In this paper, closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probability…
When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…
The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…