Sampling rate distortion is a theory for reconstructing a set of $m$ correlated signals within a desired accuracy level by randomly sampling and jointly compressing a smaller subset of $k$ signals. Which signals should be sampled and with what randomized mechanism? How should the signals be compressed, and what are optimal reconstruction algorithms? What are the tradeoffs -- under optimal processing -- among sampling procedure, compression rate and desired accuracy level? 
The sampling rate distortion function provides a precise description of the fundamental limit of optimum lossy compression rate given a desired accuracy level, together with the best sampling mechanism and processing for estimation. These tradeoffs are studied also in a universal setting, where the  underlying distribution of the signals is known only to lie in a finite family. Potential applications include in-network function computation, dynamic thermal management for onchip temperature control, and feature reconstruction.