Research

I am interested in probability theory, mathematical statistics and related areas. My interests include: distributional approximation, limit theorems, 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.

Publications:

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

  1. Christian Döbler*, Mikołaj J. Kasprzak*, Giovanni Peccati*: Functional Convergence of U-processes with Size-Dependent Kernels, Annals of Applied Probability (accepted), arXiv:1912.02705

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

  3. 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 2020, doi:10.1214/20-AIHP1049, arXiv:1710.09263, 2020

  4. 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.

  5. 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, 2020.

  6. 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), 2019.

  7. 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

Preprints:

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

  1. Christian Döbler*, Mikołaj J. Kasprzak*, Giovanni Peccati*: The multivariate functional de Jong CLT, arXiv:2104.01858

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