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Fuzzy Distribution Modeling for Synthetic Tabular Data Generation with Causality Preservation

Michael Vasilakakis, Dimitris K. Iakovidis

arXiv:2609.34349v1cs.AI

TL;DR

Tabular data's heterogeneous, non-smooth, and incomplete features challenge conventional generative models, whose interpretability is limited. This paper models feature distributions with fuzzy sets and dependencies with Fuzzy Cognitive Maps, generating samples from fuzzy concepts. It reports competitive utility, fidelity, and privacy against state-of-the-art methods, with membership-inference and attribute-disclosure attacks left for future work.

  • Problem

    Tabular data are heterogeneous, non-smooth, and often incomplete, while conventional probabilistic and deep generative models have limited interpretability.

    Source: §I · pp. 1–2

  • Method

    The framework represents feature marginals with fuzzy sets and dependencies with Fuzzy Cognitive Maps, then generates synthetic samples by sampling fuzzy concepts.

    Source: §I · p. 2

  • Results

    The approach achieves competitive utility, fidelity, and privacy across evaluated datasets compared with state-of-the-art methods.

    Source: B. Evaluation Metrics · p. 5, §IV · p. 6

  • Takeaways & Limitations

    The results support interpretable, causally grounded fuzzy modeling as a CPU-only route to competitive synthetic tabular data quality without computationally intensive deep architectures.

    Source: B. Evaluation Metrics · pp. 5–6, §IV · p. 6

    Evaluation against membership-inference and attribute-disclosure attacks is left for future work.

    Source: B. Evaluation Metrics · p. 5

Abstract

from arXiv · show

Synthetic tabular data generation provides an effective alternative for the training of machine learning models when real-world data is limited or inaccessible. However, the heterogeneous, non-smooth, and incomplete nature of tabular data poses fundamental challenges to conventional probabilistic and deep generative models, where their interpretability remains limited. This paper proposes a novel fuzzy distribution modeling methodology for synthetic tabular data generation based on fuzzy sets theory. Feature distributions are represented using fuzzy sets and feature dependencies are modeled through Fuzzy Cognitive Maps, resulting in a low-parameter, and an interpretable data representation. Synthetic samples are generated by sampling fuzzy concepts rather than raw values, enabling native support for mixed data types, missing values, and domain constraints. The methodology further supports linguistic queries and IF-THEN reasoning, facilitating transparent simulation of decision-making processes. Experimental results on benchmark datasets demonstrate competitive performance with respect to utility, fidelity and privacy compared to state-of-the-art methods, while offering substantially improved interpretability. These results establish fuzzy distribution modeling as a principled and effective approach for synthetic tabular data generation in fuzzy systems and decision support applications.

I. INTRODUCTION

Tabular synthesis is challenging because feature types and distributions vary, records may be incomplete, and features lack positional structure. The paper proposes fuzzy distribution modeling with Fuzzy Cognitive Maps (FCMs) to represent feature marginals and dependencies and generate samples from fuzzy concepts.

I. INTRODUCTION

  • Synthetic data can support model development when real-world data are limited or restricted, including privacy-preserving use and data sharing under regulatory constraints.The stated objective is to reflect real-data distributions and dependencies so models trained on synthetic data can be deployed on real-world data.Source: §I · p. 1
  • Prior approaches include neural GAN- and VAE-based models and non-neural copula, graphical-model, and tree-based methods, each with stated modeling or scalability challenges.The introduction notes that parametric copulas can struggle in high dimensions and graphical models may require prior dependency knowledge or large samples.Source: §I · p. 1
  • Tabular data combine heterogeneous feature types, non-smooth or imbalanced distributions, incomplete records, and domain-specific dependencies, with no universal transferable representation.Features also lack the inherent positional structure found in images or language.Source: §I · pp. 1–2
  • Causal structure is motivated as a way to represent feature influence beyond correlation, while FCMs model concepts and their causal relationships.The introduction states that causal structure has the potential to improve synthetic-data fidelity, consistency, and interpretability.Source: §I · p. 2
  • The framework represents feature marginals with fuzzy membership functions and dependencies with fuzzy relations, then generates samples by sampling fuzzy concepts rather than raw values.It is presented as an interpretable alternative that supports mixed data types, missing values, domain constraints, and causal reasoning through FCMs.Source: §I · p. 2

A. Data Preprocessing and Normalization

The preprocessing pipeline standardizes each feature, then rescales it to a shared [0,1] range. This produces a normalized representation for fuzzy membership functions and consistent modeling of heterogeneous features.

A. Data Preprocessing and Normalization

  • Each feature is standardized using its empirical mean and standard deviation, then linearly rescaled to [0,1] for a common universe of discourse.The z-score step reduces scale bias and improves numerical stability in the subsequent k-means clustering used to define fuzzy prototypes.Source: A. Data Preprocessing and Normalization · p. 2
  • The intermediate z-score representation reduces extreme scale differences among features before k-means clustering.The passage states that this improves numerical stability in the clustering step.Source: A. Data Preprocessing and Normalization · p. 2
  • The resulting normalized dataset facilitates fuzzy membership-function definition and consistent modeling of heterogeneous features in one framework.The normalized dataset is denoted D# in the passage.Source: A. Data Preprocessing and Normalization · p. 2

B. Fuzzy Distribution Construction

The method constructs class-specific fuzzy sets from representative feature regions and uses membership degrees to describe linguistic concepts. Their activations support FCM-mediated feature influence, while missing values can remain uncertain rather than being imputed.

B. Fuzzy Distribution Construction

  • The method treats synthetic generation as fuzzy causal reasoning and constructs fuzzy sets independently for each class to characterize features and form the fuzzy distribution.The class-specific sample subset supplies the observations used in this construction.Source: B. Fuzzy Distribution Construction · p. 2
  • Feature values are clustered within each class to identify representative regions, with cluster centers serving as linguistic values such as Low, Medium, and High.The number of clusters determines the number of linguistic values.Source: B. Fuzzy Distribution Construction · p. 2
  • Each fuzzy set uses a membership function whose triangular peak is at its cluster center and whose support extends to neighboring components.The figure passage also describes feature values activating multiple concepts to varying degrees.Source: B. Fuzzy Distribution Construction · pp. 2–3
  • Fuzzy cardinality sums membership degrees to measure a concept's effective size and representativeness within a class.Sets are ordered by cardinality so stronger linguistic concepts can activate their feature representation more fully than weaker ones.Source: B. Fuzzy Distribution Construction · p. 3
  • A data point may activate multiple membership functions across features, and this multiconcept co-activation underlies FCM-mediated influence propagation during synthesis.Fig. 2 illustrates two features with separate solid and dashed membership-function curves.Source: B. Fuzzy Distribution Construction · p. 3, Figure 2 · p. 3
  • When a feature is missing, the method makes no crisp membership assignment, leaving it partially uninstantiated and preserving uncertainty rather than imputing a value.Influence from observed features is then propagated through fuzzy cognitive reasoning.Source: B. Fuzzy Distribution Construction · p. 3

C. Modeling Feature Dependencies Using Fuzzy Cognitive

The framework models feature dependencies with a Fuzzy Cognitive Map (FCM), then propagates sampled linguistic states through it before converting them into synthetic numeric values.

C. Modeling Feature Dependencies Using Fuzzy Cognitive

  • An FCM represents concepts as feature-associated fuzzy sets and directed weighted edges as influences between concepts.The edge weights encode positive, negative, or neutral influence.Source: C. Modeling Feature Dependencies Using… · p. 3
  • Directed influence weights are estimated from fuzzy set interactions using a center-of-gravity formulation, then normalized to [−1,1].Domain knowledge may optionally constrain edge signs or existence.Source: C. Modeling Feature Dependencies Using… · p. 3
  • FCM reasoning iteratively updates concept activations until a steady state, supporting IF-THEN scenarios and samples consistent with the assumed causal influence structure.Updates use a sigmoid function that maps concept values within [0,1].Source: C. Modeling Feature Dependencies Using… · pp. 3–4
  • After propagation, stabilized activations are defuzzified into numeric features by sampling from activated membership-function supports or combining fuzzy-set centers.Membership degree biases sampling toward prototype-near values; weighted defuzzification handles multiple activated sets.Source: C. Modeling Feature Dependencies Using… · p. 4
  • Generation starts by randomly sampling membership values from learned fuzzy marginals for each feature and class, forming the initial linguistic activation vector.These activations serve as input to FCM reasoning.Source: C. Modeling Feature Dependencies Using… · p. 4

A. Experimental Setup

The evaluation compares the proposed method with three SDV synthesizers on three UCI datasets, using CPU-only experiments and consistent train/test partitions.

A. Experimental Setup

  • The evaluation aimed to compare utility of fuzzy distribution modeling with FCM against established state-of-the-art baselines under comparable computational constraints.The comparison scope was the selected CPU-trainable tabular synthesizers.Source: A. Experimental Setup · p. 4
  • Experiments ran exclusively on CPU, restricting comparisons to synthesizers reasonably trainable in CPU environments and excluding more GPU-intensive models.The stated aim was computational efficiency, fairness, and reproducibility.Source: A. Experimental Setup · p. 4
  • The proposed method was compared with SDV's Gaussian Copula, CTGAN, and TVAE using their default configurations and training-set-sized synthetic samples.The baselines represent a statistical model, an adversarial neural network, and a variational autoencoder, respectively.Source: A. Experimental Setup · p. 4
  • Evaluation used Pima Indians Diabetes, South African Heart Disease, and Statlog (German Credit), with mixed continuous and categorical attributes.Synthetic data were generated from training partitions and assessed on real test sets; model components were constructed only from training data.Source: A. Experimental Setup · p. 4

B. Evaluation Metrics

Across evaluated datasets, the FCM-based approach reports competitive utility, fidelity, and privacy, with a balanced trade-off between distributional realism and task performance. Evaluation uses TSTR classification, fidelity, and memorization-risk measures; generation propagates linguistic activations through an FCM before defuzzification.

Evaluation protocol

  • TSTR evaluates downstream utility by training a classifier on synthetic data and testing it on real data, alongside fidelity and privacy metrics.Fidelity measures cover marginal distributions, inter-feature dependencies, and aggregated statistics; privacy measures assess record memorization and exact replicas.Source: B. Evaluation Metrics · pp. 4–5

Generation procedure

  • Generation starts from randomly sampled fuzzy-concept activations, propagates them through the FCM, and converts the stabilized fuzzy state into numeric features.Defuzzification samples from dominant fuzzy-set supports, with sampling biased by membership degree; the algorithm also allows weighted combinations when multiple sets dominate.Source: B. Evaluation Metrics · p. 5

Results

  • The FCM approach consistently outperforms CTGAN and remains competitive with TVAE and Gaussian Copula on accuracy, F1-score, and AUROC.On Statlog, its AUROC is nearly identical to TVAE despite substantially lower computational complexity.Source: Table I · p. 5, B. Evaluation Metrics · p. 5

Privacy scope

  • DCR and New Row Synthesis assess memorization risk only; membership-inference and attribute-disclosure attacks are left for future work.New Row Synthesis scores are perfect across methods, while the proposed method's DCR baseline protection consistently exceeds TVAE's.Source: B. Evaluation Metrics · p. 5

Efficiency

  • The framework delivers competitive data quality under CPU-only constraints, using sparse linguistic activations and causal reasoning rather than expensive neural optimization.Although theoretical FCM size scales as O(d×E)^2, only a small subset of concepts is active and weak connections can be pruned.Source: B. Evaluation Metrics · pp. 5–6

Interpretability

  • A Diabetes example exposes each generated sample as a linguistic profile before defuzzification, making the generation process inspectable.The example profile includes High Body Mass Index, Medium Age, and Low Diastolic Blood Pressure.Source: B. Evaluation Metrics · p. 6

IV. CONCLUSION

The conclusion presents fuzzy distribution modeling with sparse FCMs as an interpretable, efficient alternative for synthetic tabular data generation. It reports competitive benchmark performance and identifies future directions for extending the framework.

Framework

  • The framework represents feature marginals with fuzzy sets and inter-feature dependencies with sparse FCMs, recasting generation as causally informed fuzzy reasoning.The resulting representation is described as interpretable, low-parameter, and computationally efficient.Source: §IV · p. 6

Results

  • Across multiple benchmark datasets, the method achieves competitive utility, fidelity, and privacy while operating exclusively on CPU.It avoids the high computational cost of deep generative models.Source: §IV · p. 6

Implications and future work

  • The authors present FCM-based fuzzy modeling as a practical alternative for resource-constrained, safety-critical, and decision-support applications.Causal reasoning is described as supporting feature coherence, transparent what-if analysis, and linguistic interpretability; future work includes automated causal-graph learning, adaptive linguistic granularity, and temporal and multi-relational data.Source: §IV · p. 6
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