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We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
We present a comprehensive ablation of nine finite-sample bound families for selective prediction with risk control, combining concentration inequalities (Hoeffding, Empirical Bernstein, Clopper-Pearson, Wasserstein DRO, CVaR) with…
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some…
We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…
Many real-world graphs have degree distributions that are well approximated by a power-law, and the corresponding scaling parameter $\alpha$ provides a compact summary of that structure which is useful for graph analysis and system…
Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
We study the spread of information in finite and infinite inhomogeneous spatial random graphs. We assume that each edge has a transmission cost that is a product of an i.i.d. random variable L and a penalty factor: edges between vertices of…
Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…
We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of…
We initiate the study of distribution testing for probability distributions over the edges of a graph, motivated by the closely related question of ``edge-distribution-free'' graph property testing. The main results of this paper are…
We study the popular distributed consensus method over networks composed of a number of densely connected clusters with a sparse connection between them. In these cluster networks, the method often constitutes two-time-scale dynamics, where…
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk…
The label propagation algorithm (LPA) has been proved to be a fast and effective method for detecting communities in large complex networks. However, its performance is subject to the non-stable and trivial solutions of the problem. In this…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
We study the statistical fluctuations of Lyapunov exponents in the discrete version of the non-integrable perturbed sine-Gordon equation, the dissipative ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations of the…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
In this paper, we investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian…