Related papers: Stein's Method for Spatial Random Graphs
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results concern both shallow random Gaussian neural networks with…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential…
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. Begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
We introduce a novel approach to Maximum A Posteriori inference based on discrete graphical models. By utilizing local Wasserstein distances for coupling assignment measures across edges of the underlying graph, a given discrete objective…
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Efficient and reliable generation of global path plans are necessary for safe execution and deployment of autonomous systems. In order to generate planning graphs which adequately resolve the topology of a given environment, many…
In this paper, we apply the Turan sieve and the simple sieve developed by R. Murty and the first author to study problems in random graph theory. In particular, we obtain upper and lower bounds on the probability of a graph on n vertices…
We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
In this paper, we establish optimal Berry--Esseen bounds for the generalized $U$-statistics. The proof is based on a new Berry--Esseen theorem for exchangeable pair approach by Stein's method under a general linearity condition setting. As…
We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…
Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…