Sensor Fusion Frameworks for Nowcasting
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
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
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
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
by applications to track disease activity of influenza and COVID-19 in the United States.
DepartmentStatistics and Data Science
- Doctor of Philosophy (PhD)