# Fake It Till You Make It: Guidelines for Effective Synthetic Data Generation
## 2 Methods: Synthetic Data Generation and Utility
### Utility Measures  
Data utility attempts to measure whether the data is appropriate for processing and analysis. There are two broad approaches for assessing the utility of a synthesized dataset: Global utility measures and analysis-specific measures [38].  
Global utility measures capture the overall utility of the synthetic dataset. The idea underpinning these measures is to offer insight into the differences in the distributions of the original and released dataset, with greater utility attributed to synthetic data that are more similar to the original data. _Distinguishability metrics_ are well-known global utility measures. They characterize the extent to which it is possible to distinguish the original dataset from the synthesized one. The most prominent distinguishability measure is the propensity score [39, 40]. Propensity score represents the probabilities of record memberships (original or synthetic). It involves building a classification model to distinguish between the real and released datasets records. A high utility implies the inability of the model to perform the distinction, it is calculated as follows [41]: The original and synthetic datasets are joined in one group with a binary indicator assigned to each record depending on whether the record is real or synthesized (1 for synthetic rows and zero for original rows). A binary classification model is constructed to discriminate between real and synthetic records. The resulting model is then used to compute the propensity score \(\hat{p}_{i}\) for each record \(i\) (predicted value for the indicator). The propensity score is calculated from the predicted value as follows:  
\[pMSE=\frac{1}{N}\sum_{i}(\hat{p}_{i}-0.5)^{2}\]  
where \(N\) is the size of the joint dataset.  
The propensity score varies between 0 and 0.25, with 0 indicating no distinguishability between the two datasets. This can happen if the generator overfits the original dataset and creates a synthetic that is indistinguishable from the original one (leading to a score of \(\hat{p}_{i}=0.5\) for every record). On the other extreme, if the two datasets are completely distinguishable, the propensity score would be 1 for synthetic rows and zero for original rows, leading to an overall score of 0.25.  
The Propensity score is cited as the most practical measure for predicting the overall utility of a synthetic dataset [25], it is also considered valuable for comparing different synthesis approaches [32].  
On the other hand, analysis specific measures assess the utility of the released data in replicating a specific analysis done on real data. The analysis can compare data summaries and/or the coefficients of models fitted to synthetic data with those from the original data. If inferences from original and synthetic data agree, then synthetic data are said to have high utility. For example, prediction accuracy assesses the utility based on the ability of the released data to replicate a prediction analysis performed on real data. Analysis specific measures do not provide an accurate measure of the overall utility, they rather focus on the specific analysis performed [27; 28; 29; 30; 34]. Still, they are widely used as a measure of synthetic data utility [28; 30; 42].  
In our experiments, we will use Prediction accuracy as an analysis specific measure. We use 4 classification algorithms to assess synthetic data utility: Logistic regression (LR), support vector machines (SM), Random forest (RF) and decision trees (DT).