Knowing when one does not know is crucial in decision making. By estimating uncertainties humans can recognize novelty both by intuition and reason, but most AI systems lack this self-reflective ability. In anomaly detection, a common approach is to train a model to learn the distinction between some notion of normal and some notion of anomalies. In contrast, we let the models build their own notion of normal by learning directly from the data in a self-supervised manner, and by introducing estimations of model uncertainty the models can recognize themselves when novel situations are encountered. In our work, the aim is to investigate the relationship between model uncertainty and anomalies in time series data. We develop a method based on a recurrent autoencoder approach, and we design an anomaly score function that aggregates model error with model uncertainty to indicate anomalies. Use the Monte Carlo Dropout as Bayesian approximation to derive model uncertainty. Asa proof of concept we evaluate our method qualitatively on real-world complex time series using stock market data. Results show that our method can identify extreme events in the stock market. We conclude that the relation between model uncertainty and anomalies can be utilized for anomaly detection in time series data.

Time series anomaly detection receives increasing research interest given the growing number of data-rich application domains. Recent additions to anomaly detection methods in research literature include deep learning algorithms. The nature and performance of these algorithms in sequence analysis enable them to learn hierarchical discriminating features and time-series temporal nature. However, their performance is affected by the speed at which the time series arrives, the use of a fixed threshold, and the assumption of Gaussian distribution on the prediction error to identify anomalous values. An exact parametric distribution is often not directly relevant in many applications and it’s often difficult to select an appropriate threshold that will differentiate anomalies with noise. Thus, implementations need the Prediction Interval (PI) that quantifies the level of uncertainty associated with the Deep Neural Network (DNN) point forecasts, which helps in making a better-informed decision and mitigates against false anomaly alerts. To achieve this, a new anomaly detection method is proposed that computes the uncertainty in estimates using quantile regression and used the quantile interval to identify anomalies. Similarly, to handle the speed at which the data arrives, an online anomaly detection method is proposed where a model is trained incrementally to adapt to the concept drift that improves prediction. This is implemented using a window-based strategy, in which a time series is broken into sliding windows of sub-sequences as input to the model. To adapt to concept drift, the model is updated when changes occur in the new arrival instances. This is achieved by using anomaly likelihood which is computed using the Q-function to define the abnormal degree of the current data point based on the previous data points. Specifically, when concept drift occurs, the proposed method will mark the current data point as anomalous. However, when the abnormal behavior continues for a longer period of time, the abnormal degree of the current data point will be low compared to the previous data points using the likelihood. As such, the current data point is added to the previous data to retrain the model which will allow the model to learn the new characteristics of the data and hence adapt to the concept changes thereby redefining the abnormal behavior. The proposed method also incorporates feature extraction to capture structural patterns in the time series. This is especially significant for multivariate time-series data, for which there is a need to capture the complex temporal dependencies that may exist between the variables. In summary, this thesis contributes to the theory, design, and development of algorithms and models for the detection of anomalies in both static and evolving time series data. Several experiments were conducted, and the results obtained indicate the significance of this research on offline and online anomaly detection in both static and evolving time-series data. In chapter 3, the newly proposed method (Deep Quantile Regression Anomaly Detection Method) is evaluated and compared with six other prediction-based anomaly detection methods that assume a normal distribution of prediction or reconstruction error for the identification of anomalies. Results in the first part of the experiment indicate that DQR-AD obtained relatively better precision than all other methods which demonstrates the capability of the method in detecting a higher number of anomalous points with low false positive rates. Also, the results show that DQR-AD is approximately 2 – 3 times better than the DeepAnT which performs better than all the remaining methods on all domains in the NAB dataset. In the second part of the experiment, sMAP dataset is used with 4-dimensional features to demonstrate the method on multivariate time-series data. Experimental result shows DQR-AD have 10% better performance than AE on three datasets (SMAP1, SMAP3, and SMAP5) and equal performance on the remaining two datasets. In chapter 5, two levels of experiments were conducted basis of false-positive rate and concept drift adaptation. In the first level of the experiment, the result shows that online DQR-AD is 18% better than both DQR-AD and VAE-LSTM on five NAB datasets. Similarly, results in the second level of the experiment show that the online DQR-AD method has better performance than five counterpart methods with a relatively 10% margin on six out of the seven NAB datasets. This result demonstrates how concept drift adaptation strategies adopted in the proposed online DQR-AD improve the performance of anomaly detection in time series. / Petroleum Technology Development Fund (PTDF)

Vehicle Path Prediction can be used to support Advanced Driver Assistance Systems (ADAS) that covers different technologies like Autonomous Braking System, Adaptive Cruise Control, etc. In this thesis, the vehicle’s future path, parameterized as 5 coordinates along the path, is predicted by using only visual data collected by a front vision sensor. This approach provides cheaper application opportunities without using different sensors. The predictions are done by deep convolutional neural networks (CNN) and the goal of the project is to use recurrent neural networks (RNN) and to investigate the benefits of using reccurence to the task. Two different approaches are used for the models. The first approach is a single-frame approach that makes predictions by using only one image frame as input and predicts the future location points of the car. The single-frame approach is the baseline model. The second approach is a sequential approach that enables the network the usage of historical information of previous image frames in order to predict the vehicle’s future path for the current frame. With this approach, the effect of using recurrence is investigated. Moreover, uncertainty is important for the model reliability. Having a small uncertainty in most of the predictions or having a high uncertainty in unfamiliar situations for the model will increase success of the model. In this project, the uncertainty estimation approach is based on capturing the uncertainty by following a method that allows to work on deep learning models. The uncertainty approach uses the same models that are defined by the first two approaches. Finally, the evaluation of the approaches are done by the mean absolute error and defining two different reasonable tolerance levels for the distance between the prediction path and the ground truth path. The difference between two tolerance levels is that the first one is a strict tolerance level and the the second one is a more relaxed tolerance level. When using strict tolerance level based on distances on test data, 36% of the predictions are accepted for single-frame model, 48% for the sequential model, 27% and 13% are accepted for single-frame and sequential models of uncertainty models. When using relaxed tolerance level on test data, 60% of the predictions are accepted by single-frame model, 67% for the sequential model, 65% and 53% are accepted for single-frame and sequential models of uncertainty models. Furthermore, by using stored information for each sequence, the methods are evaluated for different conditions such as day/night, road type and road cover. As a result, the sequential model outperforms in the majority of the evaluation results.