Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality

We consider the problem of decomposition of multiway tensor with binary entries. Such data problems arise frequently in numerous applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose that the observed binary entries follow a Bernoulli model, develop a rank-constrained likelihood-based estimation procedure, and obtain the theoretical accuracy guarantees. Specifically, we establish the error bound of the tensor estimation, and show that the obtained rate is minimax optimal under the considered model. We demonstrate the efficacy of our approach through both simulations and analyses of multiple real-world datasets on the tasks of tensor completion and clustering.