Bayesian Estimation of a Probability Mass Function Tensor with Automatic Rank Detection

Estimating the probability mass function (PMF) of a set of discrete random variables using a low-rank model for the PMF tensor has recently gained much attention. However, detecting the rank (model order) of the PMF tensor from observed data is a challenging problem. While classical techniques such as the Akaike and the Bayesian information criteria (AIC and BIC) may be applied in this regard, they require testing a number of candidate model orders before selecting the best one, a procedure which is computationally intensive for large datasets. In this work, we propose an algorithm to estimate the PMF tensor and implicitly detect its rank. We specify appropriate prior distributions for the model parameters and develop a deterministic algorithm which enables the rank to be detected as part of the inference. Numerical results using synthetic data demonstrate that, compared to classical model selection techniques, our approach is more robust against missing observations and is computationally efficient.