Related papers: Functional approximations with Stein's method of e…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov Chains whose update rules are `close enough'. We apply this technique to compare Ising models on $d$-regular expander…
We apply the Stein-Chen method to problems from extreme value theory. On the one hand, the Stein-Chen method for Poisson approximation allows us to obtain bounds on the Kolmogorov distance between the law of the maximum of i.i.d. random…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
We initiate the study of the cycle structure of uniformly random parking functions. Using the combinatorics of parking completions, we compute the asymptotic expected value of the number of cycles of any fixed length. We obtain an upper…
Generalized Brown-Resnick processes form a flexible class of stationary max-stable processes based on Gaussian random fields. With regard to applications fast and accurate simulation of these processes is an important issue. In fact,…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…
The exchange algorithm is one of the most popular extensions of the Metropolis--Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example,…
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their covariance function. In particular, we propose a new simple rate-optimal series expansion for fractional…
In this paper we give a historical account of the development of Poisson approximation using Stein's method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on…
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…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…