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We consider the problem of decomposing a higher-order tensor with binaryentries. Such data problems arise frequently in applications such asneuroimaging, recommendation system, topic modeling, and sensor networklocalization. We propose a multilinear Bernoulli model, develop arank-constrained likelihood-based estimation method, and obtain the theoreticalaccuracy guarantees. In contrast to continuous-valued problems, the binarytensor problem exhibits an interesting phase transition phenomenon according tothe signal-to-noise ratio. The error bound for the parameter tensor estimationis established, and we show that the obtained rate is minimax optimal under theconsidered model. Furthermore, we develop an alternating optimization algorithmwith convergence guarantees. The efficacy of our approach is demonstratedthrough both simulations and analyses of multiple data sets on the tasks oftensor completion and clustering.

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