  Statistical inference is the science of drawing conclusions about some system
from data. In modern signal processing and machine learning, inference is done
in very high dimension: very many unknown characteristics about the system have
to be deduced from a lot of high-dimensional noisy data. This "high-dimensional
regime" is reminiscent of statistical mechanics, which aims at describing the
macroscopic behavior of a complex system based on the knowledge of its
microscopic interactions. It is by now clear that there are many connections
between inference and statistical physics. This article aims at emphasizing
some of the deep links connecting these apparently separated disciplines
through the description of paradigmatic models of high-dimensional inference in
the language of statistical mechanics. This article has been published in the
issue on artificial intelligence of Ithaca, an Italian
popularization-of-science journal. The selected topics and references are
highly biased and not intended to be exhaustive in any ways. Its purpose is to
serve as introduction to statistical mechanics of inference through a very
specific angle that corresponds to my own tastes and limited knowledge.
