  Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural
network models that can describe multi-modal nonnegative data. NNBMs form
rectified Gaussian distributions that appear in biological neural network
models, positive matrix factorization, nonnegative matrix factorization, and so
on. In this paper, an effective inference method for NNBMs is proposed that
uses the mean-field method, referred to as the Thouless--Anderson--Palmer
equation, and the diagonal consistency method, which was recently proposed.
