Training Robust Deep Models for Time-Series Domain: Novel Algorithms and Theoretical Analysis

Despite the success of deep neural networks (DNNs) for real-world applications over time-series data such as mobile health, little is known about how to train robust DNNs for time-series domain due to its unique characteristics compared to images and text data. In this paper, we propose a novel algorithmic framework referred as RObust Training for Time-Series (RO-TS) to create robust DNNs for time-series classification tasks. Specifically, we formulate a min-max optimization problem over the model parameters by explicitly reasoning about the robustness criteria in terms of additive perturbations to time-series inputs measured by the global alignment kernel (GAK) based distance. We also show the generality and advantages of our formulation using the summation structure over time-series alignments by relating both GAK and dynamic time warping (DTW). This problem is an instance of a family of compositional min-max optimization problems, which are challenging and open with unclear theoretical guarantee. We propose a principled stochastic compositional alternating gradient descent ascent (SCAGDA) algorithm for this family of optimization problems. Unlike traditional methods for time-series that require approximate computation of distance measures, SCAGDA approximates the GAK based distance on-the-fly using a moving average approach. We theoretically analyze the convergence rate of SCAGDA and provide strong theoretical support for the estimation of GAK based distance. Our experiments on real-world benchmarks demonstrate that RO-TS creates more robust DNNs when compared to adversarial training using prior methods that rely on data augmentation or new definitions of loss functions. We also demonstrate the importance of GAK for time-series data over the Euclidean distance. The source code of RO-TS algorithms is available at https://github.com/tahabelkhouja/Robust-Training-for-Time-Series