Sequential RC-TGAN: Generating Relational Time Series with Spectral Envelope Loss

2026-06-30

AI Summary

This work addresses the challenge of modeling frequency-domain characteristics—such as periodicity and seasonality—in categorical sequences within relational time-series data. To this end, we propose the Seq. RC-TGAN framework, which introduces spectral envelope theory into generative adversarial networks for the first time. Our approach incorporates a differentiable frequency-domain loss function to explicitly preserve latent periodic structures and integrates a variational Gaussian mixture model to jointly handle both categorical and continuous variables. Key contributions include a frequency-domain regularization mechanism tailored for mixed-type time series, a benchmark dataset with theoretically grounded spectral envelope ground truth, and two novel evaluation metrics. Experimental results demonstrate that our method significantly outperforms existing models on both real-world and synthetic data, achieving superior fidelity in reproducing cyclic patterns and long-term seasonal dynamics.

Abstract

The generation of synthetic relational databases often involves modeling complex temporal dynamics, such as transaction logs or event sequences. A significant challenge in this domain is the handling of categorical time series (e.g., status codes), where standard encoding methods like one-hot encoding fail to capture intrinsic frequency-domain features such as seasonality and cyclicity. In this paper, we introduce Sequential RC-TGAN (Seq. RC-TGAN), a temporal extension of the RC-TGAN framework, equipped with a novel integrated loss function based on the \textit{Spectral Envelope Theory}. This differentiable loss allows the generator to directly optimize the preservation of latent periodic structures via backpropagation. While spectral envelope theory is inherently designed for categorical sequences, we extend this frequency-domain regularization to continuous time series by employing a Variational Gaussian Mixture Model (VGM) discretization strategy. To establish a mathematically rigorous evaluation standard, we simulate categorical time series governed by a parameter $α$, with exactly known theoretical spectral envelopes. Integrating these dynamic sequences into the child tables of a relational database yields a robust ground-truth benchmark for evaluating the frequency-domain fidelity of our generative framework. Furthermore, we address the lack of robust evaluation standards for relational time series by proposing two new metrics: Spectral Density Divergence and Spectral Envelope Divergence. Experimental results on real-world datasets, as well as our simulated benchmarks, demonstrate that our end-to-end approach significantly outperforms state-of-the-art systems in reproducing cyclic patterns and long-term seasonality across both categorical and continuous features.

Problem

• categorical time series
• spectral envelope
• relational time series
• seasonality
• frequency-domain features

Innovation

• Spectral Envelope Loss
• Sequential RC-TGAN
• Relational Time Series Generation
• Frequency-domain Regularization
• Categorical Time Series