Existing tensor completion formulation mostly relies on partial observations
from a single tensor. However, tensors extracted from real-world data are often
more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of
tensor elements are available. (ii) Coarse observation: Some tensor modes only
present coarse and aggregated patterns (e.g., monthly summary instead of daily
reports). In this paper, we are given a subset of the tensor and some
aggregated/coarse observations (along one or more modes) and seek to recover
the original fine-granular tensor with low-rank factorization. We formulate a
coupled tensor completion problem and propose an efficient Multi-resolution
Tensor Completion model (MTC) to solve the problem. Our MTC model explores
tensor mode properties and leverages the hierarchy of resolutions to
recursively initialize an optimization setup, and optimizes on the coupled
system using alternating least squares. MTC ensures low computational and space
complexity. We evaluate our model on two COVID-19 related spatio-temporal
tensors. The experiments show that MTC could provide 65.20% and 75.79%
percentage of fitness (PoF) in tensor completion with only 5% fine granular
observations, which is 27.96% relative improvement over the best baseline. To
evaluate the learned low-rank factors, we also design a tensor prediction task
for daily and cumulative disease case predictions, where MTC achieves 50% in
PoF and 30% relative improvements over the best baseline.

本文提出了一个高效的 Multi-resolution Tensor Completion Model (MTC) 来解决张量部分观测值的补全问题，该模型实现了张量模式特性的探索，并利用分辨率层次进行递归优化。在两个 COVID-19 相关的时空张量上的实验证明，MTC 可以在仅有 5% 细颗粒观测情况下提供达到 65.20% 和 75.79% 的适配度 (PoF)，相对于最佳基线的相对改进为 27.96%。