Stable and Privacy-Preserving Synthetic Educational Data with Empirical Marginals: A Copula-Based Approach

Synthetic data generation offers promise for addressing data scarcity and privacy concerns in educational technology, yet practitioners lack empirical guidance for selecting between traditional resampling techniques and modern deep learning approaches. This study presents the first systematic benchmark comparing these paradigms using a 10,000-record student performance dataset. We evaluate three resampling methods (SMOTE, Bootstrap, Random Oversampling) against three deep learning models (Autoencoder, Variational Autoencoder, Copula-GAN) across multiple dimensions: distributional fidelity (Kolmogorov-Smirnov distance, Jensen-Shannon divergence), machine learning utility such as Train-on-Synthetic-Test-on-Real scores (TSTR), and privacy preservation (Distance to Closest Record). Our findings reveal a fundamental trade-off: resampling methods achieve near-perfect utility (TSTR: 0.997) but completely fail privacy protection (DCR ~ 0.00), while deep learning models provide strong privacy guarantees (DCR ~ 1.00) at significant utility cost. Variational Autoencoders emerge as the optimal compromise, maintaining 83.3% predictive performance while ensuring complete privacy protection. We also provide actionable recommendations: use traditional resampling for internal development where privacy is controlled, and VAEs for external data sharing where privacy is paramount. This work establishes a foundational benchmark and practical decision framework for synthetic data generation in learning analytics.

Synthetic and distilled student data are increasingly used to enable privacy-conscious learning analytics, yet their suitability for decision-facing institutional support remains uncertain. In dropout support, generated data must preserve not only predictive utility or distributional resemblance, but also the financial-status evidence used to guide advising, payment-plan assistance, and scholarship-related decisions. Method: This study introduces CaP-Eval, a decision-facing causal-privacy audit workflow for evaluating generated student data under a fixed estimand, timing-aware adjustment design, estimator set, and empirical privacy-governance screen. The workflow compares original, distilled, adversarial synthetic, statistical synthetic, and DPGNet privacy-oriented generated data on predictive utility, treatment-effect fidelity, robustness to alternative estimators, and local training-record proximity. Results: DPGNet and distilled data preserved the original financial-status treatment-effect structure more reliably than the adversarial and Gaussian Copula baselines. DPGNet preserved full direction and rank agreement across epsilon levels; epsilon = 10 produced the smallest non-original IPW and DML deviations, while epsilon = 1 and epsilon = 5 amplified several financial-status contrasts. Distilled data remained highly faithful but retained the strongest local training-record proximity signal. TabularGNet preserved qualitative directions with moderate attenuation, and Gaussian Copula compressed effect magnitudes. Conclusions: Predictive utility, privacy orientation, empirical disclosure signals, and causal fidelity diverged; generated student data require joint audits of direction, magnitude, overlap, and release-governance risk before decision use.

Personalized learning systems rely on real learner data, including performance, behavior, and demographic information, but these data are highly privacy-sensitive. Differentially private (DP) synthetic data can support system development and educational research while reducing exposure of individual learners. Existing evaluations, however, assess privacy and predictive usefulness separately, without determining whether synthetic learner data remain usable for the intended personalized learning task. We introduce PEARL (Privacy-Equivalence Audit and Release Ledger), which approves a DP synthetic educational dataset only when it passes all required checks of validity, privacy protection, predictive usefulness, and suitability for the intended educational task, while recording why each rejected dataset fails. Across 96 study settings, each defined by a dataset, data-generation method, privacy budget, and random seed, only 12 produced synthetic datasets that passed all applicable PEARL checks. Many privacy-protected datasets were rejected for omitting important outcome groups, such as withdrawn students, or for failing to preserve the order of learning activities. Fairness analysis further showed that some datasets passing privacy and predictive-usefulness checks still yielded unequal at-risk prediction performance across groups defined by disability and socioeconomic background. Moreover, Deep Knowledge Tracing and Self-Attentive Knowledge Tracing learned no meaningful next-response patterns from any tested synthetic knowledge-tracing dataset, showing that privacy protection alone does not guarantee usefulness for dropout prediction, knowledge tracing, or adaptive tutoring.