Learning temporal patterns in time series remains a challenging task up until today. Particularly for anomaly detection in time series, it is essential to learn the underlying structure of a system’s normal behavior. Periodic or quasiperiodic signals with complex temporal patterns make the problem even more challenging: Anomalies may be a hard-to-detect deviation from the normal recurring pattern. In this paper, we present TCN-AE, a temporal convolutional network autoencoder based on dilated convolutions. Contrary to many other anomaly detection algorithms, TCN-AE is trained in an unsupervised manner. The algorithm demonstrates its efficacy on a comprehensive real-world anomaly benchmark comprising electrocardiogram (ECG) recordings of patients with cardiac arrhythmia. TCN-AE significantly outperforms several other unsupervised state-of-the-art anomaly detection algorithms. Moreover, we investigate the contribution of the individual enhancements and show that each new ingredient improves the overall performance on the investigated benchmark.

The training of anomaly detection models usually requires labeled data. We present in this paper a novel approach for anomaly detection in time series which trains unsupervised using a convolutional approach coupled to an autoencoder framework. After training, only a small amount of labeled data is needed to adjust the anomaly threshold. We show that our new approach outperforms several other state-of-the-art anomaly detection algorithms on a Mackey-Glass (MG) anomaly benchmark. At the same time our autoencoder is capable of learning interesting representations in latent space. Our new MG anomaly benchmark allows to create an unlimited amount of anomaly benchmark data with steerable difficulty. In this benchmark, the anomalies are well-defined, yet difficult to spot for the human eye.

This repository contains the Mackey-Glass anomaly benchmark (MGAB), which is composed of synthetic Mackey-Glass time series with non-trivial anomalies. Mackey-Glass time series are known to exhibit chaotic behavior under certain conditions. MGAB contains 10 MG time series of length 100k. Into each time series 10 anomalies are inserted with a procedure as described below. In contrast to other synthetic benchmarks, it is very hard for the human eye to distinguish the introduced anomalies from the normal (chaotic) behavior.

Real-world anomaly detection for time series is still a challenging task. This is especially true for periodic or quasi-periodic time series since automated approaches have to learn long-term correlations before they are able to detect anomalies. Electrocardiography (ECG) time series, a prominent real-world example of quasi-periodic signals, are investigated in this work. Anomaly detection algorithms often have the additional goal to identify anomalies in an unsupervised manner. In this paper we present an unsupervised time series anomaly detection algorithm. It learns with recurrent Long Short-Term Memory (LSTM) networks to predict the normal time series behavior. The prediction error on several prediction horizons is used to build a statistical model of normal behavior. We propose new methods that are essential for a successful model-building process and for a high signal-to-noise-ratio. We apply our method to the well-known MIT-BIH ECG data set and present first results. We obtain a good recall of anomalies while having a very low false alarm rate (FPR) in a fully unsupervised procedure. We compare also with other anomaly detectors (NuPic, ADVec) from the state-of-the-art.

. A new algorithm, based on the Discrete Wavelet Transform (DWT), for unsupervised anomaly detection in time series is introduced in this paper. The approach is based on using maximum likelihood estimation (MLE) on the DWT of time series. On a diverse set of 158 time series, the algorithm is compared with three other state-of-the-art anomaly detectors and it is shown to outperform the other approaches on the test set. Thanks to the linear time complexity of the DWT, our new algorithm is also computationally efficient.

An unresolved challenge for all kind of temporal data is the reliable anomaly detection, especially when adaptability is required in the case of non-stationary time series or when the nature of future anomalies is unknown or only vaguely defined. Most of the current anomaly detection algorithms follow the general idea to classify an anomaly as a significant deviation from the prediction. In this paper we present a comparative study where several online anomaly detection algorithms are compared on the large Yahoo Webscope S5 anomaly benchmark. We show that a relatively Simple Online Regression Anomaly Detector (SORAD) is quite successful compared to other anomaly detectors. We discuss the importance of several adaptive and online elements of the algorithm and their influence on the overall anomaly detection accuracy.

Learning board games by self-play has a long tradition in computational intelligence for games. Based on Tesauro's seminal success with TD-Gammon in 1994, many successful agents use temporal difference learning today. But in order to be successful with temporal difference learning on game tasks, often a careful selection of features and a large number of training games is necessary. Even for board games of moderate complexity like Connect-4, we found in previous work that a very rich initial feature set and several millions of game plays are required. In this work we investigate different approaches of online-adaptable learning rates like Incremental Delta Bar Delta (IDBD) or temporal coherence learning (TCL) whether they have the potential to speed up learning for such a complex task. We propose a new variant of TCL with geometric step size changes. We compare those algorithms with several other state-of-the-art learning rate adaptation algorithms and perform a case study on the sensitivity with respect to their meta parameters. We show that in this set of learning algorithms those with geometric step size changes outperform those other algorithms with constant step size changes. Algorithms with nonlinear output functions are slightly better than linear ones. Algorithms with geometric step size changes learn faster by a factor of 4 as compared to previously published results on the task Connect-4.

Systems that learn to play board games are often trained by self-play on the basis of temporal difference (TD) learning. Successful examples include Tesauro's well known TD-Gammon and Lucas' Othello agent. For other board games of moderate complexity like Connect Four, we found in previous work that a successful system requires a very rich initial feature set with more than half a million of weights and several millions of training games. In this work we study the benefits of eligibility traces added to this system. To the best of our knowledge, eligibility traces have not been used before for such a large system. Different versions of eligibility traces (standard, resetting, and replacing traces) are compared. We show that eligibility traces speed up the learning by a factor of two and that they increase the asymptotic playing strength.

Learning complex game functions is still a difficult task. We apply temporal difference learning (TDL), a well-known variant of the reinforcement learning approach, in combination with n-tuple networks to the game Connect-4. Our agent is trained just by self-play. It is able, for the first time, to consistently beat the optimal-playing Minimax agent (in game situations where a win is possible). The n-tuple network induces a mighty feature space: It is not necessary to design certain features, but the agent learns to select the right ones. We believe that the n-tuple network is an important ingredient for the overall success and identify several aspects that are relevant for achieving high-quality results. The architecture is sufficiently general to be applied to similar reinforcement learning tasks as well.

In this paper we present an unsupervised time series anomaly detection algorithm, which is based on the discrete wavelet transform (DWT) operating fully online. Given streaming data or time series, the algorithm iteratively computes the (causal and decimating) discrete wavelet transform. For individual frequency scales of the current DWT, the algorithm estimates the parameters of a multivariate Gaussian distribution. These parameters are adapted in an online fashion. Based on the multivariate Gaussian distributions, unusual patterns can then be detected across frequency scales, which in certain constellations indicate anomalous behavior. The algorithm is tested on a diverse set of 425 time series. A comparison to several other state-of-the-art online anomaly detectors shows that our algorithm can mostly produce results similar to the best algorithm on each dataset. It produces the highest average F1-score with one standard parameter setting. That is, it works more stable on high- and low-frequency-anomalies than all other algorithms. We believe that the wavelet transform is an important ingredient to achieve this.

Although great progress has been made in the field of computational intelligence for games in the past decades, learning board games remained a complex task until today. Machine-learning techniques – such as Temporal Difference learning (TDL) – commonly have to deal with a variety of problems when they are applied to complex board games. Although Temporal Difference learning is known as one of the successful techniques for learning board games by self-play, the success is highly dependent on the correct selection of parameters. In [37], it was shown that even with a careful selection of the parameters for a game with moderate complexity like Connect-4, learning convergence only occurs after a several million of self-play games. In this work we investigate the impact of several online-adaptable learning rates on reducing the parameter selection dependency in order to speed up the learning process. We show, that Temporal Coherence Learning (TCL) and Incremental Delta Bar Delta (IDBD) have only a small impact on the learning speed. Later, we propose a more successful approach in speeding up the learning process, called TCL-EXP with ’geometric’ learning rate changes. Additionally, we apply eligibility traces to our system for the first time. We found eligibility traces to be a very important ingredient in reducing the number of game plays required for training an almost perfect playing agent.