Tuesday, February 7, 4.15 pm, 2023. Seminar in Mathematical Statistics.

Simulation of random fields on Riemannian manifolds
Annika Lang Department of Mathematical Science, Chalmers University of Technology
Abstract:Random fields are important building blocks in spatial models disturbed by randomness such as solutions to stochastic partial differential equations. The fast simulation of random fields is therefore crucial for efficient algorithms in uncertainty quantification. In this talk I present numerical methods for Gaussian random fields on Riemannian manifolds and discuss their convergence. Simulations illustrate the theoretical findings.
This talk is based on joint work with Erik Jansson, Mihály Kovács, and Mike Pereira.
Location: Online via Zoom. Please email Krzysztof Bartoszek for invitation to Zoom meeting.

Tuesday, February 21, 3.15 pm, 2023. Seminar in Statistics.

Bayesian Borrowing Between Sub-Populations … and other topics
Carl-Fredrik Burman AstraZeneca, Göteborg
Abstract: In this seminar, we will briefly discuss a few topics from pharmaceutical statistics that may be of interest to a wider statistics / data science audience.
We will also dive a bit deeper into a problem of Bayesian borrowing of information. With the emergence of personalised medicine and targeted drugs, it is increasingly common that a drug is expected to work better in one disease subpopulation, B, than in its complement, C. If the placebo-adjusted effect in B is positive, this may spill over to a smaller but positive effect in C. Many trials are not powered to demonstrate a clear effect in C in its own right. Still, it is of great importance to determine whether the drug should receive marketing authorisation, reimbursement and wide prescriptions in C. As it makes sense to borrow information between B and C, we will explore whether a pre-specified prior for the ratio of the effects in C and B may aid the analysis and facilitate decision making. Following traditional regulatory practise, we strive to minimise assumptions. While we need an informative prior to connect the effects in C and B, we use a non-informative prior for overall efficacy.
This work triggers discussions about both Bayesian methods and information borrowing in general. Our setting constitutes one of the simplest possible situations for Bayesian borrowing. The issues that we experience in this setting, such as the discrepancy between Bayesian and frequentist approaches, the impossibility of finding a truly non-informative prior, and the type 1 error inflation, will often be issues in other more complicated situations as well.
Location: Alan Turing.

Tuesday, March 21, 3.15 pm, 2023. Seminar in Statistics.

Scaling limit of Markov chain/process Monte Carlo methods
Kengo Kamatani The Institute of Statistical Mathematics, Tokyo
Abstract: The scaling limit analysis of Markov Chain Monte Carlo methods has been a topic of intensive study in recent decades. The analysis entails determining the rate at which the Markov Chain converges to its limiting process, typically a Langevin diffusion process, and provides useful guidelines for parameter tuning. Since the seminal work of Roberts et al. in 1997, numerous researchers have generalized the original assumptions and expanded the results to more sophisticated methods. Recently, there has been growing interest in piecewise deterministic Markov processes for Monte Carlo integration methods, particularly the Bouncy Particle Sampler and the Zig-Zag Sampler. This talk will focus on determining the scaling limits for both algorithms and provide a criterion for tuning the Bouncy Particle Sampler. This is joint work with J. Bierkens (TU Delft) and G. O. Roberts (Warwick).
Location: KEY1 (Key Building).

Tuesday, April 25, 3.15 pm, 2023. Seminar in Statistics.

On the Interpretability of Regularisation for NeuralNetworks Through Model Gradient SimilarityA
Rebecka Jörnsten , Department of Mathematical Sciences, University of Gothenburg
Abstract: Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit regularisation when trained with gradient descent, often require the aid of explicit regularisers. We introduce a new framework, Model Gradient Similarity (MGS), that (1) serves as a metric of regularisation, which can be used to monitor neural network training, (2) adds insight into how explicit regularisers, while derived from widely different principles, operate via the same mechanism underneath by increasing MGS, and (3) provides the basis for a new regularisation scheme which exhibits excellent performance, especially in challenging settings such as high levels of label noise or limited sample sizes.
Authors: V. Szolnoky, V. Andersson, B. Kulcsar and R. Jörnsten
Location: Alan Turing.

Tuesday, May 2, 3.15 pm, 2023. Seminar in Statistics.

Unsupervised Learning Methods: Revealing Hidden Patterns in High-Dimensional Data through Cluster and Network Analysis
Patrik Rydén , Department of Mathematics and Mathematical Statistics, Umeå University
Abstract: Cluster analysis and network analysis are powerful unsupervised learning methods that are commonly employed in bioinformatics and systems biology to analyze complex gene expression data. By utilizing mathematical algorithms, particularly correlation-based approaches, these methods can uncover patterns and relationships within the data, such as groups of genes with similar expression patterns or genes that are highly interconnected within a biological network.
Unlike supervised classification methods, which require prior knowledge of the response data, clustering and network analysis do not rely on pre-existing information about true edges or clusters. This lack of prior knowledge makes these problems more challenging, but also provides a means of discovering hidden relationships and novel insights. These methods have been particularly valuable in addressing key medical and biological problems, such as identifying disease subgroups and predicting genetic pathways.
The identification of disease subgroups is an essential goal in precision medicine, as it allows for more personalized and targeted treatments based on individual patient characteristics. Understanding genetic pathways is also crucial for developing more effective targeted therapies for diseases.
In this talk, I will explore some common problems encountered in the use of clustering and network analysis, suggest potential solutions, and discuss methods for evaluating the efficacy of these approaches.
Location: Alan Turing.

Tuesday, May 16, 3.15 pm, 2023. Seminar in Statistics.

Some results in low-dimensional dynamics and their applications to modeling of neural activity
Justyna Signerska-Rynkowska , Dioscuri Centre in Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences
Abstract: download
Location: Alan Turing.

Tuesday, June 13, 3.15 pm, 2023. Seminar in Mathematical Statistics.

Logarithmic law of large random correlation matrices
Nestor Parolya, Delft University of Technology
Abstract: Consider a random vector y=Σ^½x, where the p elements of the vector x are i.i.d. real-valued random variables with zero mean and finite fourth moment, and Σ^½ is a deterministic p×p matrix such that the eigenvalues of the population correlation matrix R of y are uniformly bounded away from zero and infinity. In this paper, we find that the log determinant of the sample correlation matrix Ȓ based on a sample of size n from the distribution ofy satisfies a CLT (central limit theorem) for p/n→γ∈(0,1] and p≠n. Explicit formulas for the asymptotic mean and variance are provided. In case the mean of y is unknown, we show that after re-centering by the empirical mean the obtained CLT holds with a shift in the asymptotic mean. This result is of independent interest in both large dimensional random matrix theory and high-dimensional statistical literature of large sample correlation matrices for non-normal data. Finally, the obtained findings are applied for testing of uncorrelatedness of p random variables. Surprisingly, in the null case R=I, the test statistic becomes distribution-free and we show analytically that the obtained CLT also holds if the moments of order four do not exist at all, which conjectures a promising and robust test statistic for heavy-tailed high-dimensional data.
Location: Hopningspunkten.