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In this paper we generalize the 1-bit matrix completion problem to higherorder tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor$T$ in $\mathbb{R}^{N} \times \mathbb{R}^{N} \times \cdots \times\mathbb{R}^{N}$ can be estimated efficiently by only $m=O(Nd)$ binarymeasurements by regularizing its max-qnorm and M-norm as surrogates for itsrank. We prove that similar to the matrix case, i.e., when $d=2$, the samplecomplexity of recovering a low-rank tensor from 1-bit measurements of a subsetof its entries is the same as recovering it from unquantized measurements.Moreover, we show the advantage of using 1-bit tensor completion overmatricization both theoretically and numerically. Specifically, we show how the1-bit measurement model can be used for context-aware recommender systems.

Learning tensors from partial binary measurements