潜在拉普拉斯扩散用于不规则多元时间序列
Latent Laplace Diffusion for Irregular Multivariate Time Series
AI总结：
提出潜在拉普拉斯扩散（LLapDiff）生成框架，通过低维潜在轨迹和拉普拉斯域参数化实现不规则时间序列的长时预测与缺失值插补。
摘要：
不规则多元时间序列对长期预测提出了权衡：离散方法通过重新网格化可能扭曲时间结构，而连续时间模型通常需要容易漂移的序贯求解器。为弥合这一差距，我们提出了潜在拉普拉斯扩散（LLapDiff），一种生成式框架，将目标建模为低维潜在轨迹，从而无需逐步积分物理时间即可实现全范围生成。我们利用受随机端口-哈密顿动力学启发的稳定模态参数化来引导逆向过程，并通过可学习的共轭复极点参数化其在拉普拉斯域中的均值演化，从而能够在不规则时间戳上直接评估。我们还通过更新平均分析将连续动力学与不规则观测联系起来，该分析将采样间隙映射到有效事件域极点，并激发了间隙感知的历史总结器。大量实验表明，LLapDiff在长期预测中优于基线，其连续时间生成性质通过在同一模型的历史时间戳上查询，支持缺失值插补。代码可在https://github.com/pixelhero98/LLapDiffusion获取。
英文摘要：
Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
