Recovery of Future Data via Convolution Nuclear Norm Minimization
| Autor: | Guangcan Liu, Wayne Zhang |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Artificial Intelligence (cs.AI) Computer Science - Artificial Intelligence Computer Science - Information Theory Computer Vision and Pattern Recognition (cs.CV) Information Theory (cs.IT) Computer Science - Computer Vision and Pattern Recognition Library and Information Sciences Machine Learning (cs.LG) Computer Science Applications Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 69:650-665 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2022.3196707 |
| Popis: | 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. This theory provides a meaningful answer to the fundamental question of what is the minimum sampling size needed for making a given number of forecasts. Experiments on univariate time series, images and videos show encouraging results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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