Research interests

I am currently pursuing a Diploma of Advanced Studies in Data Science with specialization in Machine Learning at ETH Zurich. My topics of interest are Gaussian processes, reinforcement learning, and deep learning. I am also currently collaborating on two research projects in pure machine learning.

Geometric Gaussian processes. Defining valid kernels for Gaussian processes with values in tangent vector fields on manifolds, in particular respecting the geometry of the manifold. As an example, one can think about modelling the wind on the Earth, where the base manifold is the sphere and the wind is tangent to the surface of the Earth.
Active-measurement reinforcement learning. Developing algorithms for solving active-measurement problems, that is to say reinforcement learning problems where the agent does not automatically know its state, but can actively decide to measure it, for a cost. This has many potential applications, for instance in medical RL (where performing analyses on a patient can be expensive or even dangerous) and infrastructure monitoring and maintenance (where analyzing structural soundness of infrastructure can be very expensive).

Publications

Intrinsic Gaussian Vector Fields on Manifolds

Daniel Robert-Nicoud, Andreas Krause and Viacheslav Borovitskiy

AISTATS (2024), under review.

Various applications ranging from robotics to climate science require modeling signals on non-Euclidean domains, such as the sphere. Gaussian process models on manifolds have recently been proposed for such tasks, in particular when uncertainty quantification is needed. In the manifold setting, vector-valued signals can behave very differently from scalar-valued ones, with much of the progress so far focused on modeling the latter. The former, however, are crucial for many applications, such as modeling wind speeds or force fields of unknown dynamical systems. In this paper, we propose novel Gaussian process models for vector-valued signals on manifolds that are intrinsically defined and account for the geometry of the space in consideration. We provide computational primitives needed to deploy the resulting Hodge-Matérn Gaussian vector fields on the two-dimensional sphere and the hypertori. Further, we highlight two generalization directions: discrete two-dimensional meshes and "ideal" manifolds like hyperspheres, Lie groups, and homogeneous spaces. Finally, we show that our Gaussian vector fields constitute considerably more refined inductive biases than the extrinsic fields proposed before.

Daniel Robert-Nicoud

Research interests

Publications

Intrinsic Gaussian Vector Fields on Manifolds

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