EnTransformer: A Deep Generative Transformer for Multivariate Probabilistic Forecasting

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have recently achieved strong performance for sequence modeling, most probabilistic forecasting approaches rely on restrictive parametric likelihoods or quantile-based objectives. They can struggle to capture complex joint predictive distributions across multiple correlated time series. This work proposes EnTransformer, a deep generative forecasting framework that integrates engression, a stochastic learning paradigm for modeling conditional distributions, with the expressive sequence modeling capabilities of Transformers. The proposed approach injects stochastic noise into the model representation and optimizes an energy-based scoring objective to directly learn the conditional predictive distribution without imposing parametric assumptions. This design enables EnTransformer to generate coherent multivariate forecast trajectories while preserving Transformers' capacity to effectively model long-range temporal dependencies and cross-series interactions. We evaluate our proposed EnTransformer on several widely used benchmarks for multivariate probabilistic forecasting, including Electricity, Traffic, Solar, Taxi, KDD-cup, and Wikipedia datasets. Experimental results demonstrate that EnTransformer produces well-calibrated probabilistic forecasts and consistently outperforms the benchmark models.

Quantifying Membership Disclosure Risk for Tabular Synthetic Data Using Kernel Density Estimators

The use of synthetic data has become increasingly popular as a privacy-preserving alternative to sharing real datasets, especially in sensitive domains such as healthcare, finance, and demography. However, the privacy assurances of synthetic data are not absolute, and remain susceptible to membership inference attacks (MIAs), where adversaries aim to determine whether a specific individual was present in the dataset used to train the generator. In this work, we propose a practical and effective method to quantify membership disclosure risk in tabular synthetic datasets using kernel density estimators (KDEs). Our KDE-based approach models the distribution of nearest-neighbour distances between synthetic data and the training records, allowing probabilistic inference of membership and enabling robust evaluation via ROC curves. We propose two attack models: a 'True Distribution Attack', which assumes privileged access to training data, and a more realistic, implementable 'Realistic Attack' that uses auxiliary data without true membership labels. Empirical evaluations across four real-world datasets and six synthetic data generators demonstrate that our method consistently achieves higher F1 scores and sharper risk characterization than a prior baseline approach, without requiring computationally expensive shadow models. The proposed method provides a practical framework and metric for quantifying membership disclosure risk in synthetic data, which enables data custodians to conduct a post-generation risk assessment prior to releasing their synthetic datasets for downstream use. The datasets and codes for this study are available at https://github.com/PyCoder913/MIA-KDE.