**Speaker:** Christian Kümmerle, Assistant Professor of Computer Science, UNC Charlotte

**Title**: Learning of Transition Operators From Sparse Space-Time Samples

**Abstract**: We present a framework for solving the nonlinear inverse problem of learning a transition operator A from partial observations across different time scales. This problem is motivated by the recent interest in learning time-varying graph signals driven by graph operators which depend on the underlying topology. We show that its non-linearity can be addressed computationally by reformulating it as a matrix completion problem utilizing a low-rank property of a suitable block Hankel embedding matrix.

For a uniform and an adaptive random space-time sampling model, we quantify the recoverability of the transition operator via incoherence parameters of block Hankel embedding matrices, whose behaviors depend on the interplay between the dynamics and the graph topology for graph transition operators. We show local quadratic convergence of a suitable Iteratively Reweighted Least Squares algorithm under the two observation models from a minimal amount of samples, and present how our analysis informs a suitable adaptive sampling strategy based on a fixed budget of spatio-temporal samples. Finally, we present numerical experiments which confirm that the theoretical findings accurately track empirical phase transitions.