  The problem of identifying the phase of a given system for a certain value of
the temperature can be reformulated as a classification problem in Machine
Learning. Taking as a prototype the Ising model and using the Support Vector
Machine as a tool to classify Monte Carlo generated configurations, we show
that the critical region of the system can be clearly identified and the
symmetry that drives the transition can be reconstructed from the performance
of the learning process. The role of the discrete symmetry of the system in
obtaining this result is discussed. A finite size analysis of the learned
Support Vector Machine decision function allows us to determine the critical
temperature and critical exponents with a precision that is comparable to that
of the most efficient numerical approaches relying on a known Hamiltonian
description of the system. For the determination of the critical temperature
and of the critical exponent connected with the divergence of the correlation
length, other than the availability of a range of temperatures having
information on both phases, the method we propose does not rest on any physical
input on the system, and in particular is agnostic to its Hamiltonian, its
symmetry properties and its order parameter. Hence, our investigation provides
a first significant step in the direction of devising robust tools for
quantitative analyses of phase transitions in cases in which an order parameter
is not known.
