用扩散模型生成满足硬约束的时间序列，质量更高且可扩展。
Constrained Posterior Sampling: Time Series Generation with Hard Constraints
- 在每步去噪后将后验均值投影到约束集内，确保生成数据满足物理或领域约束。
- 在真实股票、交通和空气质量数据上，生成样本质量提升约70%，相似度提高22%。
- 支持约100个约束且无需额外训练，适合电力、交通等安全关键场景。
生成逼真的时间序列对压力测试模型和隐私保护的合成数据至关重要。在工程与安全关键应用中，这些序列必须满足特定领域或物理自然施加的硬约束。例如，生成具有峰值需求时间约束的用电量模式，可用于模拟恶劣天气下电网的运行压力。现有方法或不可扩展，或降低样本质量。为此，我们提出约束后验采样（CPS），一种基于扩散模型的采样算法，在每次去噪更新后将后验均值估计投影到约束集中。值得注意的是，CPS 可扩展至约100个约束，且无需额外训练。我们提供了理论依据，说明投影步骤对采样效果的影响。实验表明，在真实世界股票、交通和空气质量数据集上，CPS 在样本质量和与真实序列相似度上分别优于最先进方法约70%和22%。
原文摘要 · Abstract (English)
Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by physics or nature. Consider, for example, generating electricity demand patterns with constraints on peak demand times. This can be used to stress-test the functioning of power grids during adverse weather conditions. Existing approaches for generating constrained time series are either not scalable or degrade sample quality. To address these challenges, we introduce Constrained Posterior Sampling (CPS), a diffusion-based sampling algorithm that aims to project the posterior mean estimate into the constraint set after each denoising update. Notably, CPS scales to a large number of constraints ($\sim100$) without requiring additional training. We provide theoretical justifications highlighting the impact of our projection step on sampling. Empirically, CPS outperforms state-of-the-art methods in sample quality and similarity to real time series by around 70\% and 22\%, respectively, on real-world stocks, traffic, and air quality datasets.
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