## 2 Related Work  
Detecting interesting developments and anomalies in time series data in some fields of research is treated under the terms \"'trend detection\" or \"event detection\" [5; 6]. We will treat it as an \"outlier detection\" problem [7; 8]. The close relationship between those areas has been discussed earlier [9].  
Outlier detection in time series or streaming data covers a number of different types of outliers [10]. One type is outlier time series in a database of time series of equal length. Since a time series can be seen as a single point with as many dimensions as there are measurements, any traditional outlier detection method could be used [7]. By defining a similarity measure on the time series, density-based methods or cluster-based methods can find top outliers.  
Point outliers or subsequence outliers [10] are other types of outliers in time series data. These outliers are sought within a single time series or multiple time series. Ignoring the context in which the points or subsequence outliers are sought, traditional outlier detection methods can also find these types of outliers, e.g., by defining an outlier score overall subsequences of similar length.  
Another possibility is to define outlierness relative to the context, in which case they are called contextual outliers [7]. Contextual outlierness is defined relative to a context set of observations [11], e.g., a time window before or around the point. If the context is a window that includes the point itself, e.g., autoencoders can find anomalous points. Auto-encoders compress and decompress the data back to the original time series window and the reconstruction error is then used as an outlier score. For time series, LSTM auto-encoders capture timely dependencies [12]. The approach by [PERSON] et al. [12] is a semi-supervised autoencoder, that assumes access to purely normal training data, but auto-encoders can also be trained fully unsupervised on a mixture of normal and abnormal data [13]. With this approach, the assumption is that due to anomalies being underrepresented, if restricted sufficiently, the model will only fit the normal points and the reconstruction error will be larger for abnormal points or subsequences.  
Points or subsequences can also be analyzed relative to earlier measurements only. This type of outlier is rather intuitive and can be interpreted as how much the point or subsequence deviates from what was expected at a certain point in time. Novelty detection methods are of this type, since they define novelties based on prior measurements. Novelty detection methods typically do not consider temporal dependencies [14; 15].  
Looking at the temporal aspect, the obvious way to find outliers is to first predict the point or subsequence based on the past and then calculate a score that indicates how well the real values match the expected. A plethora of methods exist for time series prediction (sometimes called forecasting) [16] and any of these methods could be used. Lately, LSTMs [3] have been shown to perform better than other methods [17] and LSTMs are becoming the preferred choice for time series outlier detection (e.g., [18]).  
We apply a method similar to that of [PERSON] et al. [18], but as we cannot assume access to purely normal data, our approach is unsupervised. This introduces profound challenges, identified in Section 3.1, and requires us to purposely underfit the model similar to how autoencoders work. Additionally, we deliver outlier explanations, deploy the method in a real-life application and evaluate with real users.  
Explanation for supervised models is currently a hot topic [19; 20; 21]. Within outlier detection, a number of approaches have also been applied to explain the outlierness of found outliers (see, e.g., [22; 23; 24; 25; 26; 27; 28]), but none of these focus on contextual outliers or time-series outliers as we do.