Probabilistic non-negative tensor factorization using Markov chain Monte Carlo

We present a probabilistic model for learning non-negative tensor factorizations (NTF), in which the tensor factors are latent variables associated with each data dimension. The non-negativity constraint for the latent factors is handled by choosing priors with support on the non-negative numbers. Two Bayesian inference procedures based on Markov chain Monte Carlo sampling are described: Gibbs sampling and Hamiltonian Markov chain Monte Carlo. We evaluate the model on two food science data sets, and show that the probabilistic NTF model leads to better predictions and avoids overfitting compared to existing NTF approaches.