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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.

 

Learning nonlinear functions from input-output data pairs is one of the most fundamental problems in machine learning. Recent work has formulated the problem of learning a general nonlinear multivariate function of discrete inputs, as a tensor completion problem with smooth latent factors. We build upon this idea and utilize two ensemble learning techniques to enhance its prediction accuracy. Ensemble methods can be divided into two main groups, parallel and sequential. Bagging also known as bootstrap aggregation is a parallel ensemble method where multiple base models are trained in parallel on different subsets of the data that have been chosen randomly with replacement from the original training data. The output of these models is usually combined and a single prediction is computed using averaging. One of the most popular bagging techniques is random forests. Boosting is a sequential ensemble method where a sequence of base models are fit sequentially to modified versions of the data. Popular boosting algorithms include AdaBoost and Gradient Boosting. We develop two approaches based on these ensemble learning techniques for learning multivariate functions using the Canonical Polyadic Decomposition. We showcase the effectiveness of the proposed ensemble models on several regression tasks and report significant improvements compared to the single model. 

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general nonlinear system, as they have proven to be very effective in approximating complex highly nonlinear functions. In this work, we show that identifying a general nonlinear function y = ƒ(x1,…,xN) from input-output examples can be formulated as a tensor completion problem and under certain conditions provably correct nonlinear system identification is possible. Specifically, we model the interactions between the N input variables and the scalar output of a system by a single N-way tensor, and setup a weighted low-rank tensor completion problem with smoothness regularization which we tackle using a block coordinate descent algorithm. We extend our method to the multi-output setting and the case of partially observed data, which cannot be readily handled by neural networks. Finally, we demonstrate the effectiveness of the approach using several regression tasks including some standard benchmarks and a challenging student grade prediction task.