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Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data often are more complex due to: (i) Partial observation: Only a small subset 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. 

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations or diseases. Recovering such missing or noisy (under-reported) elements of the input tensor can be viewed as a generalized tensor completion problem. Existing tensor completion methods usually assume that i) missing elements are randomly distributed and ii) noise for each tensor element is i.i.d. zero-mean. Both assumptions can be violated for spatio-temporal tensor data. We often observe multiple versions of the input tensor with different under-reporting noise levels. The amount of noise can be time- or location-dependent as more updates are progressively introduced to the tensor. We model such dynamic data as a multi-version tensor with an extra tensor mode capturing the data updates. We propose a low-rank tensor model to predict the updates over time. We demonstrate that our method can accurately predict the ground-truth values of many real-world tensors. We obtain up to 27.2% lower root mean-squared-error compared to the best baseline method. Finally, we extend our method to track the tensor data over time, leading to significant computational savings.

 

The biological processes involved in a drug’s mechanisms of action are oftentimes dynamic, complex and difficult to discern. Time-course gene expression data is a rich source of information that can be used to unravel these complex processes, identify biomarkers of drug sensitivity and predict the response to a drug. However, the majority of previous work has not fully utilized this temporal dimension. In these studies, the gene expression data is either considered at one time-point (before the administration of the drug) or two time-points (before and after the administration of the drug). This is clearly inadequate in modeling dynamic gene–drug interactions, especially for applications such as long-term drug therapy. In this work, we present a novel REcursive Prediction (REP) framework for drug response prediction by taking advantage of time-course gene expression data. Our goal is to predict drug response values at every stage of a long-term treatment, given the expression levels of genes collected in the previous time-points. To this end, REP employs a built-in recursive structure that exploits the intrinsic time-course nature of the data and integrates past values of drug responses for subsequent predictions. It also incorporates tensor completion that can not only alleviate the impact of noise and missing data, but also predict unseen gene expression levels (GEXs). These advantages enable REP to estimate drug response at any stage of a given treatment from some GEXs measured in the beginning of the treatment. Extensive experiments on two datasets corresponding to multiple sclerosis patients treated with interferon are included to showcase the effectiveness of REP.