The topics can be defined as a long (60 ECTS) or a short (30 ECTS) thesis, unless otherwise specified.
Loss functions in machine learning
Machine learning (ML) algorithms are grounded in the cross-validation technique, in which the parameters of the model are estimated with respect to minimising a loss function. While ML algorithms are generally flexible to the choice of the loss function, standard loss functions such as the squared error are commonly used. In this case, the ML algorithm will focus on estimating the expected value of the outcome. Similarly, the pinball (or the quantile) loss function will yield an estimate of a certain quantile of the distribution of the outcome. More generally, loss functions tailored to estimate probability distributions may lead to ML algorithms that can estimate predictive uncertainty.In this project, we will investigate the role of the loss function in ML algorithms. We will focus on loss functions that yield specific user-tailored functionals, or full predictive distributions, and we will apply these methods to real-life forecasting problems. The project can be defined with the main focus on the applied aspects, or with a strong focus on the methodological aspects, depending on the interest of the student. There is potential for external collaboration.
Modelling maritime market dynamics
Maritime markets are complex dynamical systems shaped by the interaction of demand, capacity, logistical constraints, seasonality, weather, geopolitics, energy prices and market expectations. These processes operate on different timescales and often interact in nonlinear ways. This project investigates whether maritime systems can be represented through explicitly defined and semantically meaningful latent states corresponding to maritime concepts such as demand, capacity, logistical friction, sentiment and seasonality. The aim is to build models that provide insights into why predictions change, which mechanisms drive outcomes, whether the system is approaching a transition, how uncertainty propagates, and how robust the model is under structural shifts.
The project includes industrial and interdisciplinary collaboration.
Widespread risk of flooding
Water-related natural disasters like floods have a potential to cause damage over large areas once an extreme event occurs. However, traditional flood risk assessments in Norway focus on location-specific estimation of annual exceedance probabilities or warnings at the regional level that are issued for the next few days (varsom.no). In this project, we aim to describe the widespread risk of flooding in Norway through high-dimensional modelling of extremes. Specifically, we will consider a conditional approach, where we assess the probability of other locations experiencing an extreme event conditional on the value at a particular location being extreme. The individual results are then combined for assessing the overall risk structure.
Floods occur on river networks. In describing the widespread risk of floods, one thus needs to use distances on and statistical frameworks for metric graphs rather than the standard Euclidean distance.
This project can be defined with the main focus on the applied aspects, or with a strong focus on the methodological aspects, depending on the interest of the student. There is potential for a collaboration with hydrologists.