Matthieu Bulté

Hi, I'm Matt. I'm a second year PhD student in Statistics at the Department of Mathematical Science at the University of Copenhagen in Denmark.

I have a background in mathematics, with bachelor and master degrees from the Technical University of Munich. My research interest is in mathematical statistics, with a focus on statistics in non-standard spaces, machine learning, and time series analysis.

Working papers

An Autoregressive Model for Time Series of Random Objects
M. Bulté and H. Sørensen
Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. However, the absence of inherent structure in metric spaces has resulted in a literature that is predominantly non-parametric and model-free. To address this gap in models for time series of random objects, we introduce an adaptation of the classical linear autoregressive model tailored for data lying in a Hadamard space. The parameters of interest in this model are the Fréchet mean and a concentration parameter, both of which we prove can be consistently estimated from data. Additionally, we propose a test statistic and establish its asymptotic normality, thereby enabling hypothesis testing for the absence of serial dependence. Finally, we introduce a bootstrap procedure to obtain critical values for the test statistic under the null hypothesis. Our theoretical findings are illustrated by numerical studies.
Medoid splits for efficient random forests in metric spaces [link]
M. Bulté and H. Sørensen
This paper revisits an adaptation of the random forest algorithm for Fréchet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we introduce a new splitting rule that circumvents the computationally expensive operation of Fréchet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fréchet mean-based procedures and establish the consistency of the associated regression estimator. The paper provides a sound theoretical framework and a more efficient computational approach to Fréchet regression, broadening its application to non-standard data types and complex use cases.

Published papers

A practical example for the non-linear Bayesian filtering of model parameters [link]
M. Bulté, J. Latz and E. Ullmann
Appeared in Quantification of Uncertainty: Improving Efficiency and Technology (2020)
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential Importance Sampling (SIS) and Sequential Monte Carlo (SMC). Throughout the paper we illustrate the concepts and techniques with a practical example using real-world data. The task is to estimate the gravitational acceleration of the Earth g by using observations collected from a simple pendulum. Importantly, the particle filters enable the adaptive updating of the estimate for g as new observations become available. For tutorial purposes we provide the data set and a Python implementation of the particle filters.