  Data is scaling exponentially in fields ranging from genomics to neuroscience
to economics. A central question is: can modern machine learning methods be
applied to construct predictive models of natural systems like cells and brains
based on large data sets? In this paper, we examine how inference is impacted
when training data is generated by the statistical behavior of a physical
system, and hence outside direct control by the experimentalist. We develop an
information-theoretic analysis for the canonical problem of spin-network
inference. Our analysis reveals the essential role that the physical properties
of the spin network and its environment play in determining the difficulty of
the underlying machine learning problem. Specifically, stochastic fluctuations
drive a system to explore a range of configurations providing `raw' information
for a learning algorithm to construct an accurate model; yet they also blur
energetic differences between network states and thereby degrade information.
This competition leads spin networks to generically have an intrinsic optimal
temperature at which stochastic spin fluctuations provide maximal information
for discriminating among competing models, maximizing inference efficiency. We
demonstrate a simple active learning protocol that optimizes network
temperature to boost inference efficiency and dramatically increases the
efficiency of inference on a neural circuit reconstruction task. Our results
reveal a fundamental link between physics and information and show how the
physical environment can be tuned to optimize the efficiency of machine
learning.
