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Title: Modeling partially observed data with spatio-temporal dependence via regression with PDE penalization Authors:  Eleonora Arnone - Politecnico di Milano (Italy) [presenting]
Laura Sangalli - Politecnico di Milano (Italy)
Andrea Vicini - Politecnico di Milano (Italy)
Abstract: A spatio-temporal regression technique with differential regularization is studied. Through this technique, we analyze partially observed functional data with spatio-temporal dependence. We can think of spatio-temporal data as curves sampled in scattered spatial locations or surfaces observed at some time instants. The observability of these data can be of various types. For example, in the simplest case, the datum is observed uniformly in space and time. In other cases, the missing data are clustered in sub-regions. For example, we can have that, for a fixed spatial location, the corresponding curve is not observed in a long temporal interval. Vice versa, it can be the case that for a fixed time instant, the corresponding surface is not observed in a large area of the spatial domain. We focus on the partial observability characteristics of the data, and we study the proposed methodology on simulated data corresponding to different observability patterns. The methodology is suited for dealing with complicated spatial domains or signals that exhibit complex local features. Finally, we consider an application to the lake surface water temperature data. These data have a high proportion of missing values in a complex pattern, and the reconstruction of the complete signal is of great importance for climate studies.