arXiv:2608.22807cs.LGstat.ML2026-08

无需假设分布形式,即可在线检测数据分布突变。

Change Detection in Probability Flow ODE: Online Testing in Diffusion Latent Spaces

论文配图:Change Detection in Probability Flow ODE: Online Testing in Diffusion Latent Spaces
图 1 · 摘自论文原文
  • 用冻结编码器的扩散模型构建隐空间映射,将数据转为标准高斯分布。
  • 通过最大均值差异检测后验偏离,实现对任意分布突变的敏感识别。
  • 适合金融、传感器、音视频等序列数据的实时异常检测场景。

一系列时序数据任务,如金融市场趋势反转、音视频自动分段、运动传感器方向变化检测,均需识别时间序列中的分布漂移。本文研究条件分布随时间切换的变点检测问题,但前后分布均无解析表达式,传统似然比检验不适用。采用在变点前数据上训练的条件扩散模型,结合冻结的上下文编码器,通过概率流常微分方程建立确定性双射映射。变点前数据被映射至标准高斯隐空间;变点后数据经相同映射后则偏离该参考分布。使用最大均值差异(MMD)作为检验统计量,在高斯零假设下推导其闭式表达,并证明其渐近分布为退化U统计量。随后对所得统计量应用Shiryaev–Roberts在线检测方法,实现精确阈值校准。该方法可检测任意分布漂移,包括协方差旋转和高阶结构断裂,且不对任一阶段分布做参数假设。

原文摘要 · Abstract (English)

A rapidly growing range of sequential data tasks, such as identifying trend reversals in financial markets, auto-segmenting video and audio recordings, detecting changes in movement direction from motion sensors cannot be fully addressed without detection of distributional shifts in time-ordered data. We consider a sequential change-point detection problem where the conditional density switches at an unknown time, yet neither the pre- nor post-change distribution admits a closed-form. Classical likelihood-ratio statistics are inapplicable in this settings. A conditional diffusion model, trained on pre-change-point data with a frozen context encoder, defines a deterministic bijection via the probability flow ODE. Pre-change observations are mapped onto standard Gaussian latent variables. Post-change observations, processed through the same frozen map, deviate from this reference. We employ the Maximum Mean Discrepancy as the test statistic, derive closed-form expressions for its components under the Gaussian null, and establish its asymptotic distribution as a degenerate U-statistic. Afterwards we apply an online detection procedure of Shiryaev--Roberts to the resulting statistic with exact threshold calibration. The method detects arbitrary distributional shifts, including covariance rotations and higher-order structural breaks, without parametric assumptions on either regime.

分布检测扩散模型在线学习变点检测

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