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Detecting anomalies in multivariate time series(MTS) data plays an important role in many domains. The abnormal values could indicate events, medical abnormalities,cyber-attacks, or faulty devices which if left undetected could lead to significant loss of resources, capital, or human lives. In this paper, we propose a novel and innovative approach to anomaly detection called Bayesian State-Space Anomaly Detection(BSSAD). The BSSAD consists of two modules: the neural network module and the Bayesian state-space module. The design of our approach combines the strength of Bayesian state-space algorithms in predicting the next state and the effectiveness of recurrent neural networks and autoencoders in understanding the relationship between the data to achieve high accuracy in detecting anomalies. The modular design of our approach allows flexibility in implementation with the option of changing the parameters of the Bayesian state-space models or swap-ping neural network algorithms to achieve different levels of performance. In particular, we focus on using Bayesian state-space models of particle filters and ensemble Kalman filters. We conducted extensive experiments on five different datasets. The experimental results show the superior performance of our model over baselines, achieving an F1-score greater than 0.95. In addition, we also propose using a metric called MatthewCorrelation Coefficient (MCC) to obtain more comprehensive information about the accuracy of anomaly detection.

We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the construction of asymptotically valid confidence intervals for the functional, having asymptotically minimal width. One interesting consequence of our results is the discovery that, for certain functionals, the worst-case performance of our estimator may improve on that of the natural `oracle' estimator, which is given access to the values of the unknown densities at the observations.

Offline reinforcement learning aims to train a policy on a pre-recorded and fixed dataset without any additional environment interactions. There are two major challenges in this setting: (1) extrapolation error caused by approximating the value of state-action pairs not well-covered by the training data and (2) distributional shift between behavior and inference policies. One way to tackle these problems is to induce conservatism - i.e., keeping the learned policies closer to the behavioral ones. To achieve this, we build upon recent works on learning policies in latent action spaces and use a special form of Normalizing Flows for constructing a generative model, which we use as a conservative action encoder. This Normalizing Flows action encoder is pre-trained in a supervised manner on the offline dataset, and then an additional policy model - controller in the latent space - is trained via reinforcement learning. This approach avoids querying actions outside of the training dataset and therefore does not require additional regularization for out-of-dataset actions. We evaluate our method on various locomotion and navigation tasks, demonstrating that our approach outperforms recently proposed algorithms with generative action models on a large portion of datasets.

To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score -- in the online setting. This extends conformal prediction to apply to a larger class of online learning problems. Our method guarantees risk control at any user-specified level even when the underlying data distribution shifts drastically, even adversarially, over time in an unknown fashion. The technique we propose is highly flexible as it can be applied with any base online learning algorithm (e.g., a deep neural network trained online), requiring minimal implementation effort and essentially zero additional computational cost. We further extend our approach to control multiple risks simultaneously, so the prediction sets we generate are valid for all given risks. To demonstrate the utility of our method, we conduct experiments on real-world tabular time-series data sets showing that the proposed method rigorously controls various natural risks. Furthermore, we show how to construct valid intervals for an online image-depth estimation problem that previous sequential calibration schemes cannot handle.

This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be piecewise constant with densities in a H\"{o}lder class. The change points, or times at which the distribution changes, are unknown. We derive the limiting distributions of the change point estimators when the minimal jump size vanishes or remains constant, a first in the literature on change point settings. We are introducing two new features: a consistent estimator that can detect when a change is happening in data with short-term dependence, and a consistent block-type long-run variance estimator. Numerical evidence is provided to back up our theoretical results.

Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Currently, there does not exist reliable framework for discovering or describing causal chains that precede adverse hospital events. Clinically relevant and interpretable results require a framework that can (1) infer temporal interactions across multiple patient features found in EMR data (e.g., labs, vital signs, etc.) and (2) can identify patterns that precede and are specific to an impending adverse event (e.g., sepsis). In this work, we propose a linear multivariate Hawkes process model, coupled with ReLU link function, to recover a Granger Causal (GC) graph with both exciting and inhibiting effects. We develop a scalable two-phase gradient-based method to maximize a surrogate-likelihood and estimate the problem parameters, which is shown to be effective via extensive numerical simulation. Our method is subsequently extended to a data set of patients admitted to an academic level 1 trauma center located in Atalanta, GA, where the estimated GC graph identifies several highly interpretable chains that precede sepsis. Here, we demonstrate the effectiveness of our approach in learning a GC graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements.

Time series anomaly detection has applications in a wide range of research fields and applications, including manufacturing and healthcare. The presence of anomalies can indicate novel or unexpected events, such as production faults, system defects, or heart fluttering, and is therefore of particular interest. The large size and complex patterns of time series have led researchers to develop specialised deep learning models for detecting anomalous patterns. This survey focuses on providing structured and comprehensive state-of-the-art time series anomaly detection models through the use of deep learning. It providing a taxonomy based on the factors that divide anomaly detection models into different categories. Aside from describing the basic anomaly detection technique for each category, the advantages and limitations are also discussed. Furthermore, this study includes examples of deep anomaly detection in time series across various application domains in recent years. It finally summarises open issues in research and challenges faced while adopting deep anomaly detection models.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

The considerable significance of Anomaly Detection (AD) problem has recently drawn the attention of many researchers. Consequently, the number of proposed methods in this research field has been increased steadily. AD strongly correlates with the important computer vision and image processing tasks such as image/video anomaly, irregularity and sudden event detection. More recently, Deep Neural Networks (DNNs) offer a high performance set of solutions, but at the expense of a heavy computational cost. However, there is a noticeable gap between the previously proposed methods and an applicable real-word approach. Regarding the raised concerns about AD as an ongoing challenging problem, notably in images and videos, the time has come to argue over the pitfalls and prospects of methods have attempted to deal with visual AD tasks. Hereupon, in this survey we intend to conduct an in-depth investigation into the images/videos deep learning based AD methods. We also discuss current challenges and future research directions thoroughly.

The prevalence of networked sensors and actuators in many real-world systems such as smart buildings, factories, power plants, and data centers generate substantial amounts of multivariate time series data for these systems. The rich sensor data can be continuously monitored for intrusion events through anomaly detection. However, conventional threshold-based anomaly detection methods are inadequate due to the dynamic complexities of these systems, while supervised machine learning methods are unable to exploit the large amounts of data due to the lack of labeled data. On the other hand, current unsupervised machine learning approaches have not fully exploited the spatial-temporal correlation and other dependencies amongst the multiple variables (sensors/actuators) in the system for detecting anomalies. In this work, we propose an unsupervised multivariate anomaly detection method based on Generative Adversarial Networks (GANs). Instead of treating each data stream independently, our proposed MAD-GAN framework considers the entire variable set concurrently to capture the latent interactions amongst the variables. We also fully exploit both the generator and discriminator produced by the GAN, using a novel anomaly score called DR-score to detect anomalies by discrimination and reconstruction. We have tested our proposed MAD-GAN using two recent datasets collected from real-world CPS: the Secure Water Treatment (SWaT) and the Water Distribution (WADI) datasets. Our experimental results showed that the proposed MAD-GAN is effective in reporting anomalies caused by various cyber-intrusions compared in these complex real-world systems.