Research

I am interested in mathematical statistics, applied probability and related areas. My interests include: distributional approximation, limit theorems, Bayesian statistics, stochastic processes and applications to machine learning. I also like probabilistic number theory.

My DPhil research at the University of Oxford focused on applying Stein's method to functional limit results. The project was supervised by Professor Gesine Reinert.

I wrote my master's dissertation at the University of Warwick on the topic of "Erdös-Kac Theorem and mod-Poisson Convergence". The project was supervised by Dr Jon Warren.

Preprints:

1. Mikołaj J. Kasprzak, Ryan Giordano, Tamara Broderick: How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences, arXiv:2209.14992

Publications and accepted articles:

*authors listed in the alphabetical order, as is customary in pure mathematics, see here.

1. George Wynne, Mikołaj J. Kasprzak, Andrew B. Duncan: A Fourier Representation of Kernel Stein Discrepancy with Application to Goodness-of-Fit Tests for Measures on Infinite Dimensional Hilbert Spaces, Bernoulli (accepted), arXiv:2206.04552, 2023+

2. Mikołaj J. Kasprzak*, Giovanni Peccati*: Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance, Annals of Applied Probability, 33(5): 3449-3492, doi:10.1214/22-AAP1897, arXiv:2203.13137, 2023

3. Yu Wang, Mikołaj J. Kasprzak, Jonathan H. Huggins: A Targeted Accuracy Diagnostic for Variational Approximations, Proc. of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS), arXiv:2302.12419, 2023

4. Christian Döbler*, Mikołaj J. Kasprzak*, Giovanni Peccati*: The multivariate functional de Jong CLT, Probability Theory and Related Fields, 184(1): 367-399, doi:10.1007/s00440-022-01114-3,  arXiv:2104.01858, 2022

5. Christian Döbler*, Mikołaj J. Kasprzak*, Giovanni Peccati*: Functional Convergence of U-processes with Size-Dependent Kernels, Annals of Applied Probability, 32(1): 551-601, doi:10.1214/21-AAP1688, arXiv:1912.02705, 2022

6. Christian Döbler*, Mikołaj J. Kasprzak*: Stein's method of exchangeable pairs in multivariate functional approximations, Electronic Journal of Probability, 26(28):1-50, doi:10.1214/21-EJP587, arXiv:2005.12733, 2021

7. Mikołaj J. Kasprzak: Functional approximations with Stein's method of exchangeable pairs, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 56(4):2540-564, doi:10.1214/20-AIHP1049, arXiv:1710.09263, 2020

8. Mikołaj J. Kasprzak: Stein's method for multivariate Brownian approximations of sums under dependence, Stochastic Processes and Their Applications 130(8):4927-4967, doi:10.1016/j.spa.2020.02.006, arXiv:1708.02521, 2020.

9. Jonathan H. Huggins, Mikołaj J. Kasprzak, Trevor Campbell, Tamara Broderick: Validated Variational Inference via Practical Posterior Error Bounds, Proc. of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), Palermo, arXiv:1910.04102, 2020.

10. Jonathan H. Huggins, Trevor Campbell, Mikołaj J. Kasprzak, Tamara Broderick: Scalable Gaussian Process Inference with Finite-data Mean and Variance Guarantees, Proc. of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), arXiv:1806.10234, 2019.

11. Mikołaj J. Kasprzak, Andrew B. Duncan, Sebastian J. Vollmer: Note on A. Barbour’s paper on Stein’s method for diffusion approximations. Electronic Communications in Probability, Volume 22 (2017), paper no. 23, doi:10.1214/17-ECP54, 2017

Miscellanea:

1. Jonathan H. Huggins, Mikołaj J. Kasprzak, Trevor Campbell, Tamara Broderick: Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach, arXiv:1809.09505

2. Mikołaj J. Kasprzak: Diffusion approximations via Stein's method and time changes, arXiv:1701.07633

Master's dissertation: dissertation