I am a PhD student at the Image Analysis, Computational Modelling and Geometry (IMAGE) Section of The Department of Computer Science in University of Copenhagen.
My PhD thesis concerns the analysis of random objects in complex geometries arising in neuroimaging. The main focus has been in machine learning methods that provide uncertainty estimates when dealing with geometrical data. Furthermore, the geometry of such uncertainty estimates is also of interest. I am happy to have Aasa Feragen, Mads Nielsen and Tom Dela Haije as my supervisors.
My research revolves around optimal transport, Bayesian statistics and Riemannian geometry. The way these three subjects intersect in my work, is by the optimal transport framework providing a geometry for probability distributions. Under the geometric framework, we can apply manifold-valued statistics to study populations of uncertain objects. Furthermore, this geometry can be applied to advance the learning of probability distributions.
A large body of my work has also considered the so called wrapped Gaussian processes (WGPs) on Riemannian manifolds. The aim of this work was to generalize Gaussian process (GP) regression to deal with manifold-valued response variables. This way, we can incorporate a priori known geometrical constraints into statistical analysis. Taking these constraints into account has many advantages, such as not wasting resources on learning the constraints (e.g. in manifold learning), providing faithful representations for predicting new data points, and offering a family of probabilistic models that do not assign probability mass to impossible data points.
Research interests. Gaussian processes, Optimal transport, Manifold-valued statistics, Uncertainty quantification, Probabilistic numerics.
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