相关论文: Estimation of Shortest Path Covariance Matrices
We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
We study distributed algorithms built around minor-based vertex sparsifiers, and give the first algorithm in the CONGEST model for solving linear systems in graph Laplacian matrices to high accuracy. Our Laplacian solver has a round…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
The spectral gap $\gamma$ of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed…
Let $\Sigma_d^{++}$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying any two $SL_d(\mathbb{Z})$-congruent elements in $\Sigma_d^{++}$ gives rise to the space of reduced quadratic forms of…
This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine…
This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…
A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
We consider three shortest path problems in directed graphs with random arc lengths. For the first and the second problems, a risk measure is involved. While the first problem consists in finding a path minimizing this risk measure, the…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
Distributed consensus has been intensively studied in recent years as a means to mitigate state differences among dynamic nodes on a graph. It has been successfully employed in various applications, e.g., formation control of multi-robots,…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
The estimation of covariance matrices of gene expressions has many applications in cancer systems biology. Many gene expression studies, however, are hampered by low sample size and it has therefore become popular to increase sample size by…