Product Jacobi-Theta Boltzmann machines with score matching
This work addresses density estimation in machine learning, but appears incremental as it modifies an existing Boltzmann machine architecture.
The authors tackled the problem of estimating probability density functions by introducing the product Jacobi-Theta Boltzmann machine (pJTBM) as a restricted version of the Riemann-Theta Boltzmann machine (RTBM), and showed that score matching can fit densities more efficiently with pJTBM than with RTBM.
The estimation of probability density functions is a non trivial task that over the last years has been tackled with machine learning techniques. Successful applications can be obtained using models inspired by the Boltzmann machine (BM) architecture. In this manuscript, the product Jacobi-Theta Boltzmann machine (pJTBM) is introduced as a restricted version of the Riemann-Theta Boltzmann machine (RTBM) with diagonal hidden sector connection matrix. We show that score matching, based on the Fisher divergence, can be used to fit probability densities with the pJTBM more efficiently than with the original RTBM.