Abstract
Reproducing kernel Hilbert spaces (RKHS) provide a powerful framework, termed kernel mean embeddings, for representing probability distributions, enabling nonparametric statistical inference in a variety of applications. Combining RKHS formalism with Gaussian process modelling, we present a methodology to refine low-resolution (LR) spatial fields with high-resolution (HR) information. This task, known asstatistical downscaling, is challenging as the diversity of spatial datasets often prevents direct matching of observations. Yet, when LR samples are modeled as aggregate conditional means of HR samples with respect to a mediating variable that is globally observed, the recovery of the underlying fine-grained field can be framed as taking an 'inverse' of the conditional expectation, namely adeconditioning problem. Leveraging this deconditioning perspective, we introduce a Bayesian formulation of statistical downscaling able to handle potentially unmatched multi-resolution spatial fields.Bio
Alan is a final year PhD student in Statistical machine learning at the University of Oxford supervised by Prof. Dino Sejdinovic. His research interests stem across different disciplines of Machine learning application – investigating into explainability, uncertainty quantification and causal inference via kernel methods. Currently he is studying the interface between kernel methods and econometrics model.Shahine is a 2nd year DPhil student in Statistical machine learning at the University of Oxford and part of the Miracli training network, supervised by Profs. Dino Sejdinovic and Athanasios Nenes. He is interested in developing scalable and expressive statistical models allowing to account for the multiscale and multiresolution structure of climate data and better quantify our understanding of the aerosol-cloud effect on climate.
