# Unsupervised Offline Changepoint Detection Ensembles
## 1 Introduction  
Changepoint detection (CPD), being one of the stated major challenges for big data applications [1], is a particular part of an anomaly detection in time series data problem presented in detail in the fundamental works [2, 3]. In terms of the number of points, the anomalies are divided into a single point and collective ones. The changepoint detection problem mostly relates to the collective anomalies type. A common definition of the changepoint detection is proposed in [4]:  
Changepoint detection is a study of methods for identification of changes in the probability distribution of an observed stochastic process. Changepoint detection problems can be applied in many applications, such as computer network intrusions [5], power plant failures [6], finances [7], climate changing [8], and illness indication in medicine, including heart attack recognition [9] and arrhythmias detection [10]. All algorithms used for changepoint detection can be split into two main classes: \"online\" and \"offline\" algorithms. Most of the algorithms and approaches from these classes differ significantly. Online algorithms try to find changepoints as soon as they occur, and they are often applicable for real-time anomaly detection and online process monitoring. Offline algorithms appropriately deal with signal segmentation or delayed analysis of the whole process realization. Moreover, they try to solve the changepoint detection problem as accurately as possible. Some of the offline algorithms can be used in real-time batch processing. However, the offline algorithms usually lose accuracy in this case because they work only with a part of the signal and can not solve the problem for the entire signal in an optimal way. The scope of this paper is specifically an offline changepoint detection problem. Anomalies of various nature may cause different statistical changes--mean, standard deviation, autoregression dependence, seasonality, etc. To detect such changes, various specific models may be applied. One of the biggest challenges for this problem is to select either the most robust model or several better-performing ones, each for the specific statistical change. Moreover, the selection of the best model depends on the search method and selection criterion. The details regarding the model selection challenges and single-best-model paradigm are presented in [11] and references therein. Ensembles of models allow avoiding using a high number of separate models, improve the robustness of the resulting changepoint detection procedure, and reduce the dependence of the resulting procedure to the particular set of data or type of anomaly [12]. Ensemble approach in classification and clustering problems is widely studied, applied to, and formalized well [12]. In recent years, the popularity and achieved results of the ensemble approach in the outlier detection problem have grown as well. The current state of the ensemble analysis and various ensemble procedures for the outlier detection problem are represented in the following papers [12; 13; 14; 15; 16; 17]. Although outlier detection and changepoint detection problems are often considered subproblems of general anomaly detection problem, the ensemble approach in the changepoint detection problem is weakly formalized and much less highlighted. The reasons why ensemble analysis for anomaly detection subproblems is quite challenging and hence not so widely explored are well described in the mentioned paper [12]. It is worth noting that event detection in temporal data [14; 18] looks like a similar problem to changepoint detection. Nevertheless, it mainly aims at finding a single anomalous point followed by the normal points making the problem closer to the outlier detection problem. The paper [19] is the first work in the direction of changepoint detection ensembles (CPDE) for time series data according to the paper itself and to our best knowledge. We found just a few relevant papers published since 2013 [4; 11; 20; 21] that represent the current state in this field of knowledge.