Related papers: A First-Order Gradient Approach for the Connectivi…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…
Given a discrete source distribution $\mu$ and discrete target distribution $\nu$ on a common finite state space $\mathcal{X}$, we are tasked with transporting $\mu$ to $\nu$ using a given discrete-time Markov chain $X$ with the quickest…
For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems the…
SARSA is an on-policy algorithm to learn a Markov decision process policy in reinforcement learning. We investigate the SARSA algorithm with linear function approximation under the non-i.i.d.\ data, where a single sample trajectory is…
In this paper, selection of an active sensor subset for tracking a discrete time, finite state Markov chain having an unknown transition probability matrix (TPM) is considered. A total of N sensors are available for making observations of…
We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…
Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…
We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions.…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation.We study this problem in a scenario…
Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
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…
Multiplex networks are a common modeling framework for interconnected systems and multimodal data, yet we still lack fundamental insights for how multiplexity affects stochastic processes. We introduce a novel ``Markov chains of Markov…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
In a model of communication in a social network described by a simple consensus model, we pose the problem of finding a subset of nodes with given cardinality and fixed consensus values that enable the fastest convergence rate to…