Hierarchical Time Series / Grouped Time Series (HTS) google
Time series can often be naturally disaggregated in a hierarchical structure using attributes such as geographical location, product type, etc. For example, the total number of bicycles sold by a cycling warehouse can be disaggregated into a hierarchy of bicycle types. Such a warehouse will sell road bikes, mountain bikes, children bikes or hybrids. Each of these can be disaggregated into finer categories. Children’s bikes can be divided into balance bikes for children under 4 years old, single speed bikes for children between 4 and 6 and bikes for children over the age of 6. Hybrid bikes can be divided into city, commuting, comfort, and trekking bikes; and so on. Such disaggregation imposes a hierarchical structure. We refer to these as hierarchical time series. …

Maximum Variance Total Variation Denoising (MVTV) google
We consider the problem of estimating a regression function in the common situation where the number of features is small, where interpretability of the model is a high priority, and where simple linear or additive models fail to provide adequate performance. To address this problem, we present Maximum Variance Total Variation denoising (MVTV), an approach that is conceptually related both to CART and to the more recent CRISP algorithm, a state-of-the-art alternative method for interpretable nonlinear regression. MVTV divides the feature space into blocks of constant value and fits the value of all blocks jointly via a convex optimization routine. Our method is fully data-adaptive, in that it incorporates highly robust routines for tuning all hyperparameters automatically. We compare our approach against CART and CRISP via both a complexity-accuracy tradeoff metric and a human study, demonstrating that that MVTV is a more powerful and interpretable method. …

McDiarmid Drift Detection Method (MDDM) google
Increasingly, Internet of Things (IoT) domains, such as sensor networks, smart cities, and social networks, generate vast amounts of data. Such data are not only unbounded and rapidly evolving. Rather, the content thereof dynamically evolves over time, often in unforeseen ways. These variations are due to so-called concept drifts, caused by changes in the underlying data generation mechanisms. In a classification setting, concept drift causes the previously learned models to become inaccurate, unsafe and even unusable. Accordingly, concept drifts need to be detected, and handled, as soon as possible. In medical applications and military zones, for example, change in behaviors should be detected in near real-time, to avoid potential loss of life. To this end, we introduce the McDiarmid Drift Detection Method (MDDM), which utilizes McDiarmid’s inequality in order to detect concept drift. The MDDM approach proceeds by sliding a window over prediction results, and associate window entries with weights. Higher weights are assigned to the most recent entries, in order to emphasize their importance. As instances are processed, the detection algorithm compares a weighted mean of elements inside the sliding window with the maximum weighted mean observed so far. A significant difference between the two weighted means, upper-bounded by the McDiarmid inequality, implies a concept drift. Our extensive experimentation against synthetic and real-world data streams show that our novel method outperforms the state-of-the-art. Specifically, MDDM yields shorter detection delays as well as lower false negative rates, while maintaining high classification accuracies. …

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