# Process-Oriented Stream Classification Pipeline: A Literature Review
## 6 Classifier Maintenance
### Drift Detection Algorithms
#### 6.2.3 Statistical Test Based  
Within concept drift detection literature, authors often refer to statistical test-based approaches [36; 85; 155; 157]. Please note that the cited summarizing papers of this section differ in their taxonomies. Within some works, the methods listed previously also fall under statistical methods. For example, ref. [4] refer to statistical tests, which compare two windows of a data stream (see Distribution Based). Ref. [157] count statistical tests as subclasses of distribution and performance (or error)-based approaches. Ref. [85] states that numerous drift detection methods are based on Sequential Probability Ratio Tests. The idea of tests from that category is that if a distribution shifts, then the probability of observing elements of this new Distribution should be higher than the probability of observing elements of the \"old\" Distribution. An influential approach, following this idea, is the cumulative sum (CUSUM) test [36; 85; 155]. CUSUM, first proposed by [162], raises the alarm when the mean of the input data--e.g., the prediction error of the classification model (as input data of the CUSUM drift detection method researchers propose the residuals of the Kalman filter (see [36; 85; 155]))--is significantly different from a threshold value. Ref. [36] refer to multiple hypothesis testing, where parallel and hierarchical testing can be distinguished. In parallel hypothesis testing, several statistical tests are applied simultaneously to the input data stream. The algorithm Linear Four Rate drift detection (LFR) proposed by [PERSON] and [PERSON] tracks changes in the True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN) rate in parallel [163]. For each error rate, a statistical test is applied. The assumption is that error rates remain stable within a reference interval until a change occurs. Considering all kinds of error rates, the method also applies to imbalanced data sets. Additionally, different errors can be weighted higher by corresponding reference intervals.  
Hierarchical testing usually follows a two-step approach [36]. First, drifts are detected by the detection layer, and another hypothesis test is applied as a validation layer. The algorithms in the field differ in terms of the used test statistics and detection strategies. Returning to the idea of LFR, hierarchical Linear Four Rate (HLFR) is a recently proposed hierarchical drift detection algorithm. In the first step, the drift detection algorithm LFR is used as the detection layer. When a potential drift is detected, a zero-one loss test (the Zero One loss test gives the proportion of misclassified instances, where the loss of zero indicates no prediction errors) is performed on training data splits to confirm (or deny) the validity of the suspected drift. Therefore, sequentially ordered training data are split into batches. The idea is that the concept drift is confirmed when the prediction loss on the sequentially ordered training data batches deviates significantly from that of the shuffled. If the concept drift is confirmed, the upgrade of the classification model is triggered.