  We develop a method to estimate the spin-spin interactions in the Hamiltonian
from the observed magnetization curve by machine learning based on Bayesian
inference. In our method, plausible spin-spin interactions are determined by
maximizing the posterior distribution, which is the conditional probability of
the spin-spin interactions in the Hamiltonian for a given magnetization curve
with observation noise. The conditional probability is obtained by the
Markov-chain Monte Carlo simulations combined with an exchange Monte Carlo
method. The efficiency of our method is tested using synthetic magnetization
curve data, and the results show that spin-spin interactions are estimated with
a high accuracy. In particular, the relevant terms of the spin-spin
interactions are successfully selected from the redundant interaction
candidates by the $l_1$ regularization in the prior distribution.
