This paper studies the problem of time series forecasting (TSF) from the perspective of compressed sensing. First of all, we convert TSF into a more inclusive problem called tensor completion with arbitrary sampling (TCAS), which is to restore a tensor from a subset of its entries sampled in an arbitrary manner. While it is known that, in the framework of Tucker low-rankness, it is theoretically impossible to identify the target tensor based on some arbitrarily selected entries, in this work we shall show that TCAS is indeed tackleable in the light of a new concept called convolutional low-rankness, which is a generalization of the well-known Fourier sparsity. Then we introduce a convex program termed Convolution Nuclear Norm Minimization (CNNM), and we prove that CNNM succeeds in solving TCAS as long as a sampling condition--which depends on the convolution rank of the target tensor--is obeyed. Experiments on univariate time series, images and videos show encouraging results.

翻译：本文从压缩感测的角度研究时间序列预测问题。 首先,我们将TSF转换成一个更具包容性的问题,称为通过任意采样(TCAS)来加速完成,即通过任意抽样(TCAS)从一个子集的条目样本中恢复一个分数。虽然众所周知,在塔克低级框架内,理论上不可能根据某些任意选择的条目来确定目标分数,但在这项工作中,我们将表明TCS确实可以在一个称为“共和低级别”的新概念下进行处理,这个概念是众所周知的四级超市的概括化。然后,我们推出一个称为“最小化核辐射规范”(CNNM)的convex方案,并且我们证明CNNM在解决TCAS成功,只要其取样条件取决于目标的反射等级,即服从。关于单向时间序列的实验、图像和视频显示令人鼓舞的结果。