  We propose the use of Monte Carlo histogram reweighting to extrapolate
predictions of machine learning methods. In our approach, we treat the output
from a convolutional neural network as an observable in a statistical system,
enabling its extrapolation over continuous ranges in parameter space. We
demonstrate our proposal using the phase transition in the two-dimensional
Ising model. By interpreting the output of the neural network as an order
parameter, we explore connections with known observables in the system and
investigate its scaling behaviour. A finite size scaling analysis is conducted
based on quantities derived from the neural network that yields accurate
estimates for the critical exponents and the critical temperature. The method
improves the prospects of acquiring precision measurements from machine
learning in physical systems without an order parameter and those where direct
sampling in regions of parameter space might not be possible.
