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

MTC: Multiresolution Tensor Completion from Partial and Coarse Observations