相关论文: Robustness of large-scale stochastic matrices to l…

We study the algorithmic robustness of general finite Markov chains in terms of their stationary distributions to general, adversarial corruptions of the transition matrix. We show that for Markov chains admitting a spectral gap, variants…

The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…

We consider the problem of robustness in large consensus networks that occur in many areas such as distributed optimization. Robustness, in this context, is the scaling of performance measures, e.g. H2-norm, as a function of network…

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…

This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to…

Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…

We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale…

We study the worst-case communication complexity of distributed algorithms computing a path problem based on stationary distributions of random walks in a network $G$ with the caveat that $G$ is also the communication network. The problem…

The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose…

We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…

The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…

Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…

Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices…

We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…