6 citations · 10 across the 12 of their papers we have counts for
14 papers
Geometry-informed importance sampling for rare events
Qinyi Wang, Anya Katsevich, Shanyin Tong
We propose GeoIS, a new importance sampling method for estimating rare event probabilities for an underlying Gaussian distribution that exploits asymptotic theory and local event g…
Asymptotic analysis of rare events in high dimensions
Anya Katsevich, Alexander Katsevich
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis o…
A unified theory of the high-dimensional Laplace approximation with application to Bayesian inverse problems
Anya Katsevich, Vladimir Spokoiny
The Laplace approximation (LA) to posteriors is a ubiquitous tool to simplify Bayesian computation, particularly in the high-dimensional settings arising in Bayesian inverse proble…
The Laplace asymptotic expansion in high dimensions
Anya Katsevich
We prove that the classical Laplace asymptotic expansion (AE) of , extends to the high-dimensional regime in which may grow large w…
Improved dimension dependence in the Bernstein von Mises Theorem via a new Laplace approximation bound
Anya Katsevich
The Bernstein-von Mises theorem (BvM) gives conditions under which the posterior distribution of a parameter based on independent samples is asympto…
The Laplace approximation accuracy in high dimensions: a refined analysis and new skew adjustment
Anya Katsevich
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make…
Tight Bounds on the Laplace Approximation Accuracy in High Dimensions
Anya Katsevich
In Bayesian inference, a widespread technique to compute integrals against a high-dimensional posterior is to use a Gaussian proxy to the posterior known as the Laplace approximati…
On the Approximation Accuracy of Gaussian Variational Inference
Anya Katsevich, Philippe Rigollet
The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) ha…
Singular limits of certain Hilbert-Schmidt integral operators
M. Bertola, E. Blackstone, A. Katsevich +1
In this paper we study the small- spectral asymptotics of an integral operator defined on two multi-intervals and , when the multi-intervals touch each othe…
From local equilibrium to numerical PDE: Metropolis crystal surface dynamics in the rough scaling limit
Anya Katsevich
We derive the PDE governing the hydrodynamic limit of a Metropolis rate crystal surface height process in the "rough scaling" regime introduced by Marzuola and Weare. The PDE takes…
The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime
Anya Katsevich
We investigate the local equilibrium (LE) distribution of a crystal surface jump process as it approaches its hydrodynamic (continuum) limit in a nonstandard scaling regime introdu…
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models
Anya Katsevich, Afonso Bandeira
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals a…
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu +2
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and l…
On De Graaf spaces of pseudoquotients
Anya Katsevich, Piotr Mikusiński
A space of pseudoquotients is defined as equivalence classes of pairs , where is an element of a non-empty set , is an element of , a commut…