We propose Multivariate Quantile Function Forecaster (MQF2), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF2 combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF2: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure.

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is quantile crossing, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-to-sequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.

We introduce Neural Contextual Anomaly Detection (NCAD), a framework for anomaly detection on time series that scales seamlessly from the unsupervised to supervised setting, and is applicable to both univariate and multivariate time series. This is achieved by combining recent developments in representation learning for multivariate time series, with techniques for deep anomaly detection originally developed for computer vision that we tailor to the time series setting. Our window-based approach facilitates learning the boundary between normal and anomalous classes by injecting generic synthetic anomalies into the available data. NCAD can effectively take advantage of domain knowledge and of any available training labels. We demonstrate empirically on standard benchmark datasets that our approach obtains a state-of-the-art performance in the supervised, semi-supervised, and unsupervised settings.

The Internet of Things (IoT) can be considered as Service Oriented Architecture (SOA) of Microservices (μS). The μSs inherently process data that affects the privacy, safety, and security of its users. IoT service security is a key challenge. Most state of the art providing IoT system security is policy based. We showcase a graph-based access control that runs as module on IoT nodes, or in the network. Our solution intercepts and firewalls inter-service communication. It automatically creates a model of legitimate communication relationships. The model is interactively updated via a simple-to-understand interface. Our solution adds inevitable IoT security to existing IoT systems.