Variance Reduction in Training Forecasting Models with Subgroup Sampling

In real-world applications of large-scale time series, one often encounters the situation where the temporal patterns of time series, while drifting over time, differ from one another in the same dataset. In this paper, we provably show under such heterogeneity, training a forecasting model with commonly used stochastic optimizers (e.g. SGD) potentially suffers large gradient variance, and thus requires long time training. To alleviate this issue, we propose a sampling strategy named Subgroup Sampling, which mitigates the large variance via sampling over pre-grouped time series. We further introduce SCott, a variance reduced SGD-style optimizer that co-designs subgroup sampling with the control variate method. In theory, we provide the convergence guarantee of SCott on smooth non-convex objectives. Empirically, we evaluate SCott and other baseline optimizers on both synthetic and real-world time series forecasting problems, and show SCott converges faster with respect to both iterations and wall clock time. Additionally, we show two SCott variants that can speed up Adam and Adagrad without compromising generalization of forecasting models.

Improve black-box sequential anomaly detector relevancy with limited user feedback

Anomaly detectors are often designed to catch statistical anomalies. End-users typically do not have interest in all of the detected outliers, but only those relevant to their application. Given an existing black-box sequential anomaly detector, this paper proposes a method to improve its user relevancy using a small number of human feedback. As our first contribution, the method is agnostic to the detector: it only assumes access to its anomaly scores, without requirement on any additional information inside it. Inspired by a fact that anomalies are of different types, our approach identifies these types and utilizes user feedback to assign relevancy to types. This relevancy score, as our second contribution, is used to adjust the subsequent anomaly selection process. Empirical results on synthetic and real-world datasets show that our approach yields significant improvements on precision and recall over a range of anomaly detectors.