Spatial applications of Markov random fields and neural networks for spatio-temporal denoising, causal inference and reinforcement learning

Discrete spatial structures are ubiquitous in statistical analysis. They can take the form of images, grids, and more generally, graphs. This work develops novel methodology leading to broadly applicable algorithms of graph smoothing and neural newtorks to improve statistical learning in a variety of tasks and spatially-structured domains, including temporal and sequential decision-making processes. Thus, each chapter corresponds to a case study with applications in spatio-temporal denoising, causal inference, and reinforcement learning. Graph smoothing methods are used in all of them and their effectiveness is evaluated. In addition, some chapters develop more specialized methods that further exploit the spatial and statistical structure of the data. One of the objectives sustained throughout the work will be developing scalable algorithms to handle high-resolution spatial data or other computationally demanding scenarios.Statistic