My research interests lie in high-dimensional probability theory and its applications in the mathematics of data science, machine learning, and signal processing. I’m currently interested in
- randomized data dimension reduction methods, using structured random matrices and random hyperplane tessellations;
- theory for deep learning, e.g., properties of the initialization (random neural nets) and memorization capacity;
- high-dimensional covariance estimation, motivated by wireless communication with massive multiple input multiple output (MIMO) antenna systems;
- statistical postprocessing of weather forecasts using a combination of statistics and machine learning, in collaboration with the Royal Netherlands Meteorological Institute (KNMI).
In the past I’ve worked on
- compressed sensing, with a focus on deriving reconstruction results in scenarios with randomized measurement models (Fourier and circulant-type measurements) and coarse analog-to-digital quantization (one-bit compressed sensing);
- sharp estimates for martingales, stochastic integrals, and stochastic convolutions in Banach spaces, motivated by the semigroup approach to stochastic PDEs with Lévy and martingale noise;
- noncommutative analysis in the context of von Neumann algebras (noncommutative Banach function spaces, noncommutative interpolation theory, noncommutative probability theory) and Banach algebras (crossed products).
These research directions are now dormant.