16 citations · 84 across the 16 of their papers we have counts for
17 papers
Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds
Vahe Karagulyan, Mikołaj Kasprzak, Pierre Alquier
We study the minimax estimation of the pseudo-spectral gap of a Markov chain from the observation of a single trajectory. Extending earlier works on finite-state space cha…
Quantitative Error Bounds for Scaling Limits of Stochastic Iterative Algorithms
Xiaoyu Wang, Mikolaj J. Kasprzak, Jeffrey Negrea +2
Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in…
A Targeted Accuracy Diagnostic for Variational Approximations
Yu Wang, Mikołaj Kasprzak, Jonathan H. Huggins
Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models w…
How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences
Mikołaj J. Kasprzak, Ryan Giordano, Tamara Broderick
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But app…
A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces
George Wynne, Mikołaj Kasprzak, Andrew B. Duncan
Kernel Stein discrepancy (KSD) is a widely used kernel-based measure of discrepancy between probability measures. It is often employed in the scenario where a user has a collection…
Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance
Mikołaj J. Kasprzak, Giovanni Peccati
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound…
Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap
Emilia Pompe, Mikołaj J. Kasprzak, Pierre E. Jacob
Bayesian inference provides a framework to combine various model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources.…
The multivariate functional de Jong CLT
Christian Döbler, Mikołaj Kasprzak, Giovanni Peccati
We prove a multivariate functional version of de Jong's CLT (1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical proc…
Stein's method of exchangeable pairs in multivariate functional approximations
Christian Döbler, Mikołaj J. Kasprzak
In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approxima…
Functional Convergence of Sequential U-processes with Size-Dependent Kernels
Christian Döbler, Mikołaj Kasprzak, Giovanni Peccati
We consider sequences of -processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of ana…
Validated Variational Inference via Practical Posterior Error Bounds
Jonathan H. Huggins, Mikołaj Kasprzak, Trevor Campbell +1
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to th…
Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach
Jonathan H. Huggins, Trevor Campbell, Mikołaj Kasprzak +1
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is…
Scalable Gaussian Process Inference with Finite-data Mean and Variance Guarantees
Jonathan H. Huggins, Trevor Campbell, Mikołaj Kasprzak +1
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack…
Functional approximations with Stein's method of exchangeable pairs
Mikolaj J. Kasprzak
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian ap…
Stein's method for multivariate Brownian approximations of sums under dependence
Mikołaj J. Kasprzak
We use Stein's method to obtain a bound on the distance between scaled -dimensional random walks and a -dimensional (correlated) Brownian Motion. We consider dependence schem…
Note on A. Barbour's paper on Stein's method for diffusion approximations
Mikolaj J. Kasprzak, Andrew B. Duncan, Sebastian J. Vollmer
In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's me…
Diffusion approximations via Stein's method and time changes
Mikolaj J. Kasprzak
We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then…