  A vast array of transformative technologies developed over the past decade
has enabled measurement and perturbation at ever increasing scale, yet our
understanding of many systems remains limited by experimental capacity.
Overcoming this limitation is not simply a matter of reducing costs with
existing approaches; for complex biological systems it will likely never be
possible to comprehensively measure and perturb every combination of variables
of interest. There is, however, a growing body of work - much of it
foundational and precedent setting - that extracts a surprising amount of
information from highly under sampled data. For a wide array of biological
questions, especially the study of genetic interactions, approaches like these
will be crucial to obtain a comprehensive understanding. Yet, there is no
coherent framework that unifies these methods, provides a rigorous mathematical
foundation to understand their limitations and capabilities, allows us to
understand through a common lens their surprising successes, and suggests how
we might crystalize the key concepts to transform experimental biology. Here,
we review prior work on this topic - both the biology and the mathematical
foundations of randomization and low dimensional inference - and propose a
general framework to make data collection in a wide array of studies vastly
more efficient using random experiments and composite experiments.
