Beyond the Signs: Nonparametric Tensor Completion via Sign Series

01/31/2021
by   Chanwoo Lee, et al.
0

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign 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- and high-rank signals, while encompassing many existing tensor models – including CP models, Tucker models, single index models, several hypergraphon models – as special cases. We show that the sign tensor series is theoretically characterized, and computationally estimable, via classification tasks with carefully-specified weights. Excess risk bounds, estimation error rates, and sample complexities are established. We demonstrate the outperformance of our approach over previous methods on two datasets, one on human brain connectivity networks and the other on topic data mining.

READ FULL TEXT
research
05/04/2021

Nonparametric Trace Regression in High Dimensions via Sign Series Representation

Learning of matrix-valued data has recently surged in a range of scienti...
research
02/16/2020

Tensor denoising and completion based on ordinal observations

Higher-order tensors arise frequently in applications such as neuroimagi...
research
03/14/2022

Noisy Tensor Completion via Low-rank Tensor Ring

Tensor completion is a fundamental tool for incomplete data analysis, wh...
research
01/01/2021

TenIPS: Inverse Propensity Sampling for Tensor Completion

Tensors are widely used to represent multiway arrays of data. The recove...
research
05/08/2022

GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion

Low-rank tensor factorization or completion is well-studied and applied ...
research
03/31/2017

Fundamental Conditions for Low-CP-Rank Tensor Completion

We consider the problem of low canonical polyadic (CP) rank tensor compl...
research
10/01/2021

Applying Differential Privacy to Tensor Completion

Tensor completion aims at filling the missing or unobserved entries base...

Please sign up or login with your details

Forgot password? Click here to reset