Prediction Optimization of Interrelated Time Series

Abstract: Time series forecasting is a useful tool for predicting future events based on past recorded signals. Such analysis is common in a variety of application domains including healthcare, power grid management, and financial markets. In such domains, collections of multiple interrelated time series (e.g., one series per patient, building, or stock) often require selecting a forecasting model per series. Optimizing a model per series separately is computationally prohibitive, often leading to sub-optimal solutions, such as fixing a single model configuration for all time series. In this work we propose to reframe the per-series model-selection problem as a recommender-system task over a partially observed validation-loss matrix. We introduce ITSOP, a meta-learning framework that evaluates a subset of series-model pairs and uses collaborative filtering and hybrid recommendation methods to infer unobserved validation losses and select, for each series, the model with the lowest predicted loss. We offer an analysis of the empirical prediction risk and derive sample-complexity bounds on the order of magnitude of the number of series–model evaluations required to reliably infer the validation loss matrix. A thorough empirical analysis shows ITSOP to outperform state-of-the-art meta-learning baselines and quantifies empirically the train set size for effective prediction