Mikolaj Kasprzak - Stein's method and Gaussian process approximations
| Dates: | 27 April 2022 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Mikolaj Kasprzak (University of Luxembourg) will speak in the Probability seminar.
Functional limit theorems have found multiple applications in fields ranging from statistical changepoint detection to probabilistic population genetics. In the field of machine learning, analysing Gaussian processes arising as functional limits of stochastic gradient algorithms has recently been proposed as a method to approximately compute their mixing times and averaged-process distributions. However, functional approximations are rarely equipped with theoretical guarantees on their quality, which limits their practical applicability. At the same time, Gaussian processes are commonly applied as models in numerous areas, including that of functional data analysis. Unfortunately, tools for testing goodness of fit to Gaussian processes are not widely available in the litarature, which makes functional data analysts unable to accurately assess how good their modelling choices are.
In this talk, I will present results (proved using Stein's method) which can be considered as initial steps towards building a theory for quantifying the error in functional Gaussian process approximations. I will show how those initial results may be used to analyse the rate of functional convergence of sequences of weighted U-statistics. I will also talk about an upcoming work on Gaussian Process goodness-of-fit testing using Stein's method on Hilbert spaces and its applicability to functional data analysis problems. On the theoretical side, I will describe different ways in which one can use Stein's method in the context of infinite-dimensional distributions and build infinite-dimensional Stein discrepancies.
The talk will be based on multiple results obtained together with Christian Döbler, Andrew Duncan, Giovanni Peccati and George Wynne.
Travel and Contact Information
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https://zoom.us/j/95434478825
