# Fast Performance Modeling across Different Database Versions Using Partitioned Co-Kriging
## 4 Partitioned Co-Kriging Based Performance Prediction  
### Overview  
Our goal is to construct an accurate performance prediction model using a small sample in target domain. To overcome the challenge of insufficient sample, we reuse prior information that we can get from source domain to learn a performance model more efficiently. The foundation of our method is that performance responses in source and target have high correlations. Thus, the large samples in source can be applied to build a performance model in target. The performance prediction is realized by the co-kriging method.  
The assumption of co-kriging method is that the performance response is stationary. In practice, the performance response of database is not stationary in the entire configuration space, but it is relatively smooth in different regions. Based on this characteristic, we propose to learn performance prediction models within each region. Therefore, we first need to solve the partition problem: how to divide the entire configuration space into several smooth regions?  
Figure 2: Performance models exhibit similarities across different database versions.  
Generally, there are only sparse samples in target due to the high cost in collecting the samples. The small samples provide too little information to perform the partitioning task. In contrast, the sample in source is usually readily available. As a consequence, we use the concept of relatedness between source and target to address the problem. The partition of configuration space can be achieved by clustering with the adequate samples from source domain. The prediction accuracy can be improved effectively by using this partition scheme.  
Figure 3 illustrates the performance prediction process for unseen configurations in target. The input of PCK method incorporates performance measurements from both source and target. We use random sampling method to generate a small number of samples in target, while a large number of samples are available in source. According to the database performance characteristics, we consider dividing the entire configuration space into several smooth regions by clustering the sufficient performance measurements in source. With the region information of source samples, each target sample can determines its region by Euclidean distance. A target sample adopt the region information of a source sample which has the nearest Euclidean distance with it. Subsequently, we can learn corresponding performance models in different regions using all the samples and the partition information in configuration space. Finally, we can estimate the performance value for any unseen configuration with this performance prediction model.  
In summary, we propose an innovative way of fast performance modeling in updated databases (never database versions) using co-kriging. It makes use of the large number of source samples in two ways: (1) the abundant and easily accessible source samples can be reused to facilitate the construction of an accurate performance model, and (2) they can further provide partition information about the smooth region in configuration space due to the correlation of source and target, thus improve the prediction accuracy of the co-kriging-based prediction model.