相关论文: Estimation of Shortest Path Covariance Matrices

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…

Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition…

We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…

The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…

This work provides a unified analysis of the properties of the sample covariance matrix $\Sigma_n$ over the class of $p\times p$ population covariance matrices $\Sigma$ of reduced effective rank $r_e(\Sigma)$. This class includes scaled…

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…

This work presents a detailed covariance and correlation matrix analysis for experimentally measured cross sections obtained using the activation technique. Both statistical and systematic contributions to the covariance matrix were…

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

This paper details a new algorithm to solve the shortest path problem in valued graphs. Its complexity is $O(D \log v)$ where $D$ is the graph diameter and $v$ its number of vertices. This complexity has to be compared to the one of the…

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…

We consider spatial stochastic models, which can be applied e.g. to telecommunication networks with two hierarchy levels. In particular, we consider two Cox processes concentrated on the edge set of a random tessellation, where the points…

Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…

Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…

Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…