BeyondtheSigns: NonparametricTensor CompletionviaSignSeries

A nonparametric approach to tensor completion is developed based on anewmodel which we coin assign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low-andhigh-rank signals, while encompassing manyexisting tensor models-- includingCPmodels,Tuckermodels,singleindexmodels,structuredtensorswith repeating entries--as special cases. We provably reduce the tensor estimation problem to a series of structured classification tasks, and we develop a learning reduction machinery to empower existing low-rank tensor algorithms for more challenging high-rank estimation.