Misc,
Statistical physics of inference: Thresholds and algorithms
(Mar 8, 2016)
Abstract
Many questions of fundamental interest in todays science can be formulated as
inference problems: Some partial, or noisy, observations are performed over a
set of variables and the goal is to recover, or infer, the values of the
variables based on the indirect information contained in the measurements. For
such problems, the central scientific questions are: Under what conditions is
the information contained in the measurements sufficient for a satisfactory
inference to be possible? What are the most efficient algorithms for this task?
A growing body of work has shown that often we can understand and locate these
fundamental barriers by thinking of them as phase transitions in the sense of
statistical physics. Moreover, it turned out that we can use the gained
physical insight to develop new promising algorithms. Connection between
inference and statistical physics is currently witnessing an impressive
renaissance and we review here the current state-of-the-art, with a pedagogical
focus on the Ising model which formulated as an inference problem we call the
planted spin glass. In terms of applications we review two classes of problems:
(i) inference of clusters on graphs and networks, with community detection as a
special case and (ii) estimating a signal from its noisy linear measurements,
with compressed sensing as a case of sparse estimation. Our goal is to provide
a pedagogical review for researchers in physics and other fields interested in
this fascinating topic.
