Appendix for " Beyond the Signs: Nonparametric Tensor Completion via Sign Series "

The appendix consists of proofs (Section A), additional theoretical results (Section B), and numerical experiments (Section C). When g is strictly increasing, the mapping x7 g(x) is sign preserving. Specifically, if x 0, then g(x) g(0) = 0. Conversely, ifg(x) 0 = g(0), then applying g 1 to both sides givesx 0. When g is strictly decreasing, the mappingx7 g(x) is sign reversing. See Section B.2 for constructive examples. Based on the definition of classification lossL(,), the function Risk() relies only on the sign pattern of the tensor.