Constrained Posterior Sampling: Time Series Generation with Hard Constraints

TL;DR

This paper introduces Constrained Posterior Sampling (CPS), a scalable diffusion-based method for generating realistic, constrained time series data that outperforms existing approaches in quality and similarity.

Contribution

The paper presents CPS, a novel diffusion-based sampling algorithm capable of handling numerous hard constraints without additional training, with theoretical and empirical validation.

Findings

CPS scales to approximately 100 constraints without retraining.

CPS improves sample quality by around 70% over state-of-the-art methods.

CPS increases similarity to real data by about 22%.

Abstract

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.