  In an age of exponentially increasing data generation, performing inference
tasks by utilizing the available information in its entirety is not always an
affordable option. The present paper puts forth approaches to render tracking
of large-scale dynamic processes via a Kalman filter affordable, by processing
a reduced number of data. Three distinct methods are introduced for reducing
the number of data involved in the correction step of the filter. Towards this
goal, the first two methods employ random projections and innovation-based
censoring to effect dimensionality reduction and measurement selection
respectively. The third method achieves reduced complexity by leveraging
sequential processing of observations and selecting a few informative updates
based on an information-theoretic metric. Simulations on synthetic data,
compare the proposed methods with competing alternatives, and corroborate their
efficacy in terms of estimation accuracy over complexity reduction. Finally,
monitoring large networks is considered as an application domain, with the
proposed methods tested on Kronecker graphs to evaluate their efficiency in
tracking traffic matrices and time-varying link costs.
