Related papers: Sample path large deviations for queueing networks…

Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…

We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random…

Modeling networks as different graph types and researching on route finding strategies, to avoid congestion in dense subnetworks via graph-theoretic approaches, contributes to overall blocking probability reduction in networks. Our main…

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…

Big Data has become the primary source of understanding the structure and dynamics of the society at large scale. The network of social interactions can be considered as a multiplex, where each layer corresponds to one communication channel…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

In a class of methods for measurement of available path capacity and other capacity-related metrics in a network, trains of probe packets are transmitted from a sender to a receiver across a network path, and the sequences of time stamps at…

We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…

We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…

Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…

In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity.…

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…

Data on vehicular mobility patterns have proved useful in many contexts. Yet generative models which accurately reproduce these mobility patterns are scarce. Here, we explore if recurrent neural networks can cure this scarcity. By training…

We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…

The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

We prove that the long term distribution of the queue length process in an ergodic generalised Jackson network obeys the Large Deviation Principle with a deviation function given by the quasipotential. The latter is related to the unique…