# Challenges of Using Synthetic Data Generation Methods for Tabular Microdata
## 2 Materials and Methods
This metric quantifies the likelihood that the \(i\)-th record in the original data has a smaller weighted distance to its nearest synthetic observation (\(\hat{r}_{i}\)) than to its nearest real observation (\(r_{i}\)), with \(\epsilon\) representing the threshold of closeness. For all occurrences where the measurement \(\hat{r}_{i}\) is smaller than \(r_{i}\), we calculate the proportion of these occurrences. Generating high-quality synthetic data can be computationally intensive, necessitating substantial computational resources. The experiments in this study, conducted on a robust server setup, underscore the resource demands associated with SDG. Utilizing NVIDIA H100 PCIe 80 GB graphics cards and Intel Xeon Silver 4416+ processors, along with a significant amount of RAM (1008 GB), highlights the need for powerful hardware to handle the complex computations involved in SDG. Such resources enable the processing of large datasets and the implementation of advanced models, which are critical for ensuring the quality and accuracy of synthetic data. This computational intensity is a crucial consideration for researchers and organizations aiming to employ SDG methods, as it necessitates access to high-performance computing infrastructure to achieve optimal results. In addition to the SDG methods evaluated in our benchmark, we also considered two additional methods: ADS-GAN [6] and PATE-GAN [21]. ADS-GAN (Anonymization through Data Synthesis Generative Adversarial Network) is a framework developed to address privacy concerns by generating synthetic data that closely resemble real data while protecting sensitive information. Like traditional GANs, the generator creates synthetic data (\(\mathbf{\hat{x}}\)) by taking a real dataset (\(\mathbf{x}\)) and random noise (\(\mathbf{z}\)) as input. Additionally, an identifiability loss is calculated to assess how similar the synthetic data are to the real data, measured by the weighted Euclidean distance \(\mathbb{E}_{x,\mathbf{\hat{x}}|x}[-\|w(\mathbf{x}-\hat{x})\|]\). This similarity is controlled by a parameter called Lambda (see Algorithm 1 in [6]), which dictates the allowable similarity between the datasets. A higher value for Lambda allows the generator to deviate more from a specific distribution, resulting in more private generated data. PATE-GAN (Private Aggregation of Teacher Ensembles Generative Adversarial Network) is another framework designed to address privacy concerns in GANs. First, multiple teacher models \(\mathbf{T}_{1},\mathbf{T}_{2},\dots,\ \mathbf{T}_{k}\) are trained on disjoint partitions of the real data. Each teacher learns to classify the data into different categories, contributing to an ensemble of diverse classifiers. When presented with a new data sample, each teacher independently provides its classification. To preserve privacy, these individual outputs are aggregated using a noise mechanism. This noisy aggregation ensures that no single teacher's decision dominates and leaks sensitive information. A student model (the generator in the GAN framework) is trained using the aggregated teacher outputs as labels. The student's objective is to generate synthetic data that resemble the real data as closely as possible while minimizing the privacy risk. Only a student is trained to avoid directly involving the teachers in the optimization algorithm, as they are trained on the real data, and their parameter values could reveal substantial information about the real data. We have opted not to include both approaches in our evaluation due to problems encountered in their respective implementations during internal evaluations. Nonetheless, we include them in our discussion to highlight the challenges associated with GANs (see also [22] for a more non-technical view on this).