**Time series prediction problems are becoming increasingly high-dimensional in modern applications, such as climatology and demand forecasting. For example, in the latter problem, the number of items for which demand needs to be forecast might be as large as 50,000. In addition, the data is generally noisy and full of missing values. Thus, modern applications require methods that are highly scalable, and can deal with noisy data in terms of corruptions or missing values. However, classical time series methods usually fall short of handling these issues. In this paper, we present a temporal regularized matrix factorization (TRMF) framework which supports data-driven temporal learning and forecasting. We develop novel regularization schemes and use scalable matrix factorization methods that are eminently suited for high-dimensional time series data that has many missing values. Our proposed TRMF is highly general, and subsumes many existing approaches for time series analysis. We make interesting connections to graph regularization methods in the context of learning the dependencies in an autoregressive framework. Experimental results show the superiority of TRMF in terms of scalability and prediction quality. In particular, TRMF is two orders of magnitude faster than other methods on a problem of dimension 50,000, and generates better forecasts on real-world datasets such as Wal-mart E-commerce datasets.**

*Abstract:*### Citation

- Temporal Regularized Matrix Factorization for High-dimensional Time Series Prediction

H. Yu, N. Rao, I. Dhillon.

To appear in*Neural Information Processing Systems (NIPS)*, December 2016.*Bibtex:*