Minimizing response time in time series classification

Providing a timely output is one of the important criteria in applications of time series classification. Recent studies have been motivated to explore models of early prediction, prediction based on truncated temporal observations. The truncation of input improves the response time, but generally reduces the reliability of the prediction. The trade-off between the earliness and the accuracy is an inherent challenge of learning an early prediction model. In this paper, we present an optimization-based approach for learning an ensemble model for timely prediction with an intuitive objective function. The proposed model is comprised of time series classifiers with different response time, and a sequential aggregation procedure to determine the single timing of its output. We formalize the training of the ensemble classifier as a quadratic programming problem and present an iterative algorithm which minimizes an empirical risk function and the response time required to achieve the minimal risk simultaneously. We conduct an empirical study using a collection of behavior and time series datasets to evaluate the proposed algorithm. In the comparisons of the traditional and time-sensitive performance measures, the ensemble framework showed significant advantages over the existing methods on early prediction.