Rafal Kulik

Full Professor in the Department of Mathematics and Statistics at the University of Ottawa.

Postal address:
Rafal Kulik
Department of Mathematics and Statistics
University of Ottawa
STEM Complex
150 Louis Pasteur Private
K1N 6N5 Ottawa, Ontario
Canada

Office: Room STM 553

Email: rkulik@uottawa.ca

What's new?

  • June 2025: I am a member of the Scientific Committee of the 14th International Conference on Extreme Value Analysis to be held at the University of North Carolina in June 2025.
  • October 2024: A final report on Office of the Privacy Commissioner of Canada Contributions Program 2023-24 project is available here.
  • October 2024: Devyani Biswal defended her PhD on Contributions to Probabilistic and Statistical Foundations of Differential Privacy.
  • October 2024: A paper "A remarkable example on clustering of extremes for regularly-varying stochastic processes" with with S. Bai and Y. Wang has been submitted. See .pdf file on Arxiv.org.
  • August 2024: I co-organized a workshop Mathematics, Statistics, and Geometry of Extreme Events in High Dimensions in Mathematisches Forschungsinstitut in Oberwolfach (Germany).
  • June 2024: Bartosz Glowacki (PhD student) received a prize for an oral presentation during The Twelfth Annual Canadian Statistics Student Conference.
  • A paper "Integral Functionals and the Bootstrap for the Tail Empirical Process: with with G. Ivanoff and H. Loukrati has been published in Extremes 26, 1-41, (2023).
    Final version available at Extremes webpage.

Current research projects

  • NSERC Discovery Grant Extremes of Complex Data Structures: Probabilistic Properties and Statistical Inference (2024-2029). See details.
  • Data privacy (See details.)
    • MITACS project Statistical framework and methodology for risk and privacy in complex and high-dimensional data (2023-2027).
    • Office of the Privacy Commissioner project Benchmarking Large Language Models and Privacy Protection (2024-2025).

Recent papers

  • with S. Bai and Y. Wang, A remarkable example on clustering of extremes for regularly-varying stochastic processes. Submitted (2024). .pdf file on Arxiv.org.
  • with Z. Chen, Asymptotic expansions for blocks estimators: PoT framework. Submitted (2023). .pdf file on Arxiv.org.
  • with Z. Chen, Limit theorems for unbounded cluster functionals of regularly varying time series. Submitted (2023). .pdf file on Arxiv.org.
  • with P. Kokoszka, Principal component analysis of infinite variance functional data. Journal of Multivariate Analysis 193, (2023).
    Final version available at JMVA webpage.
  • with G. Ivanoff and H. Loukrati, Integral Functionals and the Bootstrap for the Tail Empirical Process. Extremes 26, 1-41, (2023).
    Final version available at Extremes webpage.
  • with Y. Cissokho, Estimation of cluster functionals for regularly varying time series: sliding blocks estimators. Electronic Journal of Statistics 15(1), 2777-2831, (2021).
    Final version available at EJS webpage.
  • with Y. Cissokho, Estimation of cluster functionals for regularly varying time series: Runs estimators. Electronic Journal of Statistics 16(1), 3561-3607, (2021).
    Final version available at EJS webpage.

Students

  • Devyani Biswal defended her PhD on Contributions to Probabilistic and Statistical Foundations of Differential Privacy (October 2024).
  • Current PDF students: Mai Ghannam (co-supervised with Stanislav Volgushev). Topic: Block maxima method for non-stationary time series. PDF supported by CANSSI Distinguished Postdoctoral Fellowships program.
  • Current PhD students:
    • Bartosz Glowacki. Topic: Extreme Value Theory for Machine Learning algorithms.
    • Yizhen Teng. Topic: Differential Privacy for Machine Learning algorithms.
    • Chang Qu. Topic: TBA.
  • Current MSc students:
    • Heidi Barriault. Topic: Extremal Quantile Regression: Estimation and Model Selection.

Teaching (Winter 2024)

MAT4374/5182 Computational Statistics

MAT4376B/5314B Topics in Statistics: High-dimensional Data Analysis

MAT4376G/5314G Topics in Statistics: Foundations of Data Privacy



Refer to BrightSpace for details.

Research:

I do a research in probability and statistics, in particular:
- Limit theorems for weakly and strongly dependent random variables
- Time series, especially long memory and heavy tailed time series
- Extreme value theory for time series
- Extreme value theory for Machine Learning algorithms
- Probabilistic and Statistical aspects of Differential Privacy

Here you can find my papers and preprints, co-authors etc.

More details on Extreme Value Theory projects.

More details on Data Privacy projects.

Books

Some admin duties