Online Forecasting Matrix Factorization

We consider the problem of forecasting a high-dimensional time series that can be modeled as matrices where each column denotes a measurement and use low-rank matrix factorization for predicting future values or imputing missing ones. We define and analyze our problem in the online setting in which the data arrive as a stream and only a single pass is allowed. We present and analyze new matrix factorization techniques that can learn low-dimensional embeddings effectively in an online manner. Based on these embeddings, we derive a recursive minimum mean square error estimator based on an autoregressive model. Experiments with two real datasets of tens of millions of measurements show the benefits of the proposed approach.