Sensor Fusion Frameworks for Nowcasting

<p>A fundamental task in many online time series settings is to estimate the finalized value of a signal that will only be fully observed at a later time. The goal in nowcasting is to produce such estimates using contemporaneous</p> <p>information; this differs from the task of forecasting, which learns from past data to predict future values. In this thesis, we study sensor fusion (SF), a sequential nowcasting framework derived from a process-agnostic Kalman filter (KF), and detail two (mathematically equivalent)   reformulations: first to the standard KF itself via an augmented measurement space, and then to an equality-constrained regression problem. We leverage these</p> <p>equivalences to port several established ideas (e.g., regularization schemes) in regression to dynamical systems. In settings where only convolved outcomes of the signal can be observed, several new challenges arise: (i) deconvolution to infer the latent state, (ii) subsequent uncertainty propagation through SF, and (iii) reconvolution</p> <p>frameworks to evaluate performance. Towards solving these challenges, we introduce new methodology to perform and evaluate real-time nowcasting by deconvolution with specialized regularization techniques, which can prepend the SF framework. We motivate our work throughout</p> <p>by applications to track disease activity of influenza and COVID-19 in the United States.</p>