Generating Synthetic Relational Tabular Data via Structural Causal Models (2025)

Abstract: Synthetic tabular data generation has received increasing attention in recent years, particularly with the emergence of foundation models for tabular data. The breakthrough success of TabPFN (Hollmann et al.,2025), which leverages vast quantities of synthetic tabular datasets derived from structural causal models (SCMs), demonstrates the critical role synthetic data plays in developing powerful tabular foundation models. However, most real-world tabular data exists in relational formats spanning multiple interconnected tables — a structure not adequately addressed by current generation methods. In this work, we extend the SCM-based approach by developing a novel framework that generates realistic synthetic relational tabular data including causal relationships across tables. Our experiments confirm that this framework is able to construct relational datasets with complex inter-table dependencies mimicking real-world scenarios.

## introduction the development of synthetic data generation techniques has seen remarkable progress with the advent of foundation models, particularly in domains such as images and text. however, generating realistic tabular data -especially relational tabular data with properly linked entries -remains an underexplored challenge in machine learning research. while large language models and diffusion models have revolutionized synthetic data generation across various domains, structured tabular data has received comparatively less attention despite its prevalence in real-world applications. in this paper, we develop a novel synthetic relational data generation framework for creating arbitrarily large amounts of relational datasets with complex, realistic dependencies, suitable, e.g., for foundation model training and benchmark creation. in order to systematically model both intra-table correlations and inter-table relationships, our method constructs data independently from real-world datasets, overcoming accessibility limitations. our method is inspired by the scmbased approach for single tables of tabpfn @xcite . however, we introduce critical changes to the original scm framework, and extend it to generate multiple tables connected through shared key columns. based on these extensions, we provide an automated framework for creating synthetic relational datasets that comprise both statistical properties within individual tables and structural relationships between them. this contribution enables the creation of realistic relational tabular data that can be used for developing models capturing inter-table relationships. ## related work synthetic tabular data generation has evolved significantly to address challenges like data scarcity and privacy concerns. earlier work @xcite presented the synthetic data vault, which builds generative models of relational databases through recursive conditional parameter aggregation. it is the first learning-based approach for generating relational data. recently, @xcite proposed an approach that combines graph neural network embeddings with diffusion models, exploiting a graph representation of relational data induced by foreign key constraints. the method captures topological structure and statistical properties across multiple linked tables. these approaches require a (real-world) dataset as a basis to extract statistical and relational patterns, which are then used to generate new data with the same statistical properties. however, due to the lack of accessible real-world datasets, these methods seem to be unsuited for producing huge amounts of relational datasets with manifold intra-and inter-table relationships. a generation method independent of real-world data was proposed in @xcite , generating synthetic datasets through scms @xcite , which naturally allow for simulating wide-ranging causal dependencies. however, the method is restricted to single, unrelated tables. ## data generation method our structured data generation approach is based on an scm, represented by a directed acyclic graph (dag) g with directed edges, connecting parent nodes (causes) to child nodes (effects). for every node @xmath0, . . . , n , a structural assignment ## extensions to relational data this section extends the previously described methodology to generate relational tables, summarized in algorithm 2. the objective is to create algorithm 2 generating relational datasets sample dags g main and g add connect via coupling node c: g @xmath1.r.t. algorithm 1 for merged graph sample dataset w.r.t. algorithm 1 for g add (incl. c) two tables with different sample sizes that share a common feature, represented as a coupling node. first, we independently sample two dags, denoted by g main and g add , according to the procedure described in subsection 3.1. then, we introduce a coupling node c that is caused by a sink of g add and directs to a feature of g main . in this way, we establish a relationship between these graphs and assure, that information propagates from g add to g main . to incorporate latent causal influence from g add to g main , we connect feature nodes of g add to target nodes of g main . an example of two coupled graphs is illustrated in fig. 2 . nodes belonging to the main graph g main are labeled m1, m2, . . ., forming the same graph as shown in fig. 1 . the nodes in the additional graph g add are denoted by a1, a2, . . .. in the same way, more than two relational tables can be generated. the data samples are generated once for the merged graph (including node c) and once for graph g add (including node c), both with separate sample sizes. although we utilize the merged graph to generate the data together with the (latent) causal relationships, the main table contains only the data corresponding to the nodes of g main (including node c). the headers of the resulting main and additional tables for the example graphs of fig. 2 are presented in tables 1 and 2 . the edges representing the latent causality effectively link the two tables. consequently, a comprehensive understanding of the affected targets requires integrating information from both tables, as demonstrated in section 5. without the latent causality links, the information propagated through node c would be sufficient to represent the relationships in g main . ## evaluation we exemplary analyze one relational dataset consisting of two coupled tables constructed as stated in section 4. this example dataset is based on the dag shown in fig. 2 . we sample the main dataset with 100,000 rows, described and illustrated in appendix a and in order to perform regression or classification tasks for several target columns, we compute taskindependent table entry embeddings with respect to the embdi procedure @xcite , for a variety of embedding dimensions. first, we consider the main table only. for each training row, we compute a row embedding vector by averaging the embeddings of all entries in this row, excluding the target columns to be task-independent. this row embedding procedure can be applied not only to training rows but also to test rows, as the entries in the test rows are drawn from the same underlying distribution as the entries in the training rows. for all target columns, we then perform a regression or classification task, depending on the type of pooling function (numerical as mean, median, norm, ... or categorical). for any test row, we search for 10 nearest neighbors in the row embedding space of the training rows. the prediction is computed as an average of the target values of the selected 10 training rows, weighted by the inverse distance of the test row embedding vector to the 10 nearest training row embedding vectors. the quality of the prediction is measured by the root-mean-squared error (rmse) for numerical targets and by the area under the receiver operating characteristic curve (auc) for categorical targets. these quality measures for two nodes of the example dataset are shown in red in fig. 3 with respect to the embedding dimension. second, we apply the embdi embedding procedure to the main and additional table simultaneously. we use all the rows of the additional table for training, while for the main table we reserve 10% for testing as before. again, regression and classification tasks are conducted for the target columns of the main table. the results for the two selected nodes are highlighted in green in fig. 3 . as the merged information requires a higher embedding dimension to be fully represented, the comparison of the two curves in fig. 3 is meaningful for sufficiently high embedding dimensions. there, involving the additional table improves the results for targets influenced by latent information from the additional dataset. hence, we showed that our method for synthetic relational dataset generation is able to construct realistic related tables in the sense that the additional table contains information that is not present in the main table, but influences the target columns of the main table. this is an essential, frequently occurring property of real-world relational datasets. we emphasize that further research should include a more comprehensive evaluation with more datasets and further methods for downstream tasks, see section 7. ## discussion and conclusion in this work, we presented an approach for generating relational datasets based on scms. the corresponding graph controls the causality between features and targets, involving latent causal relationships to model inter-table dependencies. our approach serves as a scalable methodology to provide huge amount of data with various statistical properties for robust training of a tabular foundation model for relational tabular data. the main advantage to use scms is the ability to model causal relationships. thus, we are able to control the dependence between certain targets and features. additionally, by incorporating isolated sub-graphs, we can generate data that is irrelevant to the targets mimicking real-world redundancy. the quality of generated data is determined by several parameters. choosing a large hidden dimension n and projecting the data to a one-dimensional output may significantly increase the difficulty of predicting a target based on the feature nodes. furthermore, the choice of the activation function of the neural networks influences data complexity. a key strength of our approach lies in its ability to generate relational tables that capture complex causal relationships, including those mediated by latent variables. this simulation of inter-table dependencies, often lacking in simpler methods, is crucial for developing robust table representation learning models that can effectively handle the complexities of real-world data, commonly encountered in database management systems.