The research group in Mathematical Statistics and Data Science studies advanced methods and models for analysing and representing data. We employ probability theory and stochastic processes to rigorously model uncertainty and randomness, and abstract and linear algebra to understand the structure of statistical models and the relationships between their parameters.
 |
Pauliina Ilmonen Professor Multivariate extreme values, functional data analysis, cancer epidemiology |
 |
Kaie Kubjas Associate Professor Algebraic statistics |
 |
Lasse Leskelä Associate Professor Mathematical statistics, network analysis, probability theory |
 |
Vanni Noferini Associate Professor Network analysis, random matrix theory |
 |
Jukka Kohonen University Lecturer Statistics, combinatorics |
 |
Pekka Pere University Lecturer Statistics |
 |
Jonas Tölle Senior University Lecturer Stochastic processes, probability theory |
Hawkes processes are a class of mutually exciting temporal point processes where past events may increase the probability of future events. A multivariate Hawkes process consists of multiple interacting point processes, referred to as components. Each component has a conditional intensity that depends on the joint history of all components. Components can be partitioned into communities, defined as sets that share interaction parameters. The objective of the thesis is to develop a community detection method for stationary, symmetrically interacting Hawkes processes with light-tailed memory kernels. The latent community structure is shown to be encoded in the second-order cumulant of the process. The proposed method is based on applying spectral clustering to an estimator of the second-order cumulant. The main contribution of the thesis is a non-asymptotic, high-probability bound on the proportion of misclassified components. This result is obtained by developing a concentration inequality for the cumulant estimator as an extension of existing results for Hawkes process cumulants, and combining it with recovery guarantees for spectral clustering. The performance of the proposed method is illustrated on simulated data.
 |
 |
 |
Page content by: webmaster-math [at] list [dot] aalto [dot] fi