# Interpretation for Variational Autoencoder Used to Generate Financial Synthetic Tabular Data
###### Abstract  
Synthetic data, artificially generated by computer programs, has become more widely used in the financial domain to mitigate privacy concerns. Variational Autoencoder (VAE) is one of the most popular deep-learning models for generating synthetic data. However, VAE is often considered a \"black box\" due to its opaqueness. Although some studies have been conducted to provide explanatory insights into VAE, research focusing on explaining how the input data could influence VAE to create synthetic data, especially for tabular data, is still lacking. However, in the financial industry, most data are stored in a tabular format. This paper proposes a sensitivity-based method to assess the impact of inputted tabular data on how VAE synthesizes data. This sensitivity-based method can provide both global and local interpretations efficiently and intuitively. To test this method, a simulated dataset and three Kaggle banking tabular datasets were employed. The results confirmed the applicability of this proposed method. interpretability; variational autoencoder; financial synthetic tabular data; sensitivity-based method; feature importance; feature interaction +
Footnote †: journal:  
0000-0001-1409-2221-1111-1111-1111-1111-1111-1111-1111-1111-1111-1111-1111-1111-1111-1111-11111-1111-11111-1111-11111-1111-11111-1111-1111-11  
and mimicking, which adds randomness to a dataset [4]. However, one significant disadvantage of these statistical techniques is that the relationship between different columns cannot be well preserved. Hence, the method of sampling new data from joint distributions learned from an original dataset was proposed [5]. Although joint distributions can capture some potential connections between columns in a tabular dataset, the difficulty of learning all the joint distributions and relationships of a tabular dataset would increase as the complexity of the dataset increases. Even though statistical approaches, playing dominant roles in synthetic data generation for a long time in the past, are fast and easy to implement, a more robust model to tackle the complexity of data is especially needed for the banking industry, where the datasets are usually complex. Recent advancements in deep learning have made generative algorithms more popular for data synthesis [5]. Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) are two deep-learning models that are commonly used for synthetic data generation [6]. Although GANs have been proven to generate more realistic images compared with VAEs in synthetic image data generation, the same cannot be assumed for synthetic tabular data generation in financial applications [7]. A study compares the performance of VAEs and GANs in generating synthetic tabular data, showing that while GANs outperform VAEs in synthesizing mostly categorical data types, VAEs perform better in synthesizing continuous data types and datasets with a mix of continuous and categorical data [8]. As financial datasets are often mixed datasets containing continuous data and categorical variables, this paper focuses on studying VAEs for synthetic tabular data generation. Despite their superior performance, deep-learning models such as the VAE are usually labelled as \"black boxes\" due to their opaqueness [9]. Data scientists cannot explain the reasons behind the decisions made by the deep-learning models to the fullest extent. However, in reality, the interpretability of deep-learning models is crucial for the scientists who invent the model, the software developers who implement the model, and the clients influenced by the model. This calls for building trust toward the deep-learning models [10]. In VAEs, understanding the decision-making process or the synthetic data generation process is inextricably linked to the latent representation/space of a VAE since synthetic data is produced by using the latent representation that captures the critical information of input data [11].