  We propose an inference method to estimate sparse interactions and biases
according to Boltzmann machine learning. The basis of this method is $L_1$
regularization, which is often used in compressed sensing, a technique for
reconstructing sparse input signals from undersampled outputs. $L_1$
regularization impedes the simple application of the gradient method, which
optimizes the cost function that leads to accurate estimations, owing to the
cost function's lack of smoothness. In this study, we utilize the majorizer
minimization method, which is a well-known technique implemented in
optimization problems, to avoid the non-smoothness of the cost function. By
using the majorizer minimization method, we elucidate essentially relevant
biases and interactions from given data with seemingly strongly-correlated
components.
