Related papers: Analytical approach to network inference: Investig…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the…
We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the…
Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…
Convolutional Neural Networks are a well-known staple of modern image classification. However, it can be difficult to assess the quality and robustness of such models. Deep models are known to perform well on a given training and estimation…
Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that…
Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual…
A key question in many network studies is whether the observed correlations between units are primarily due to contagion or latent confounding. Here, we study this question using a segregated graph (Shpitser, 2015) representation of these…
We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts…
We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…
Binary density ratio estimation (DRE), the problem of estimating the ratio $p_1/p_2$ given their empirical samples, provides the foundation for many state-of-the-art machine learning algorithms such as contrastive representation learning…