发表机构
National Research University Higher School of Economics; The University of Sydney Business School; CIREQ; CEBDA（国立研究型大学高等经济学院; 悉尼大学商学院; 蒙特利尔数量经济学研究中心; 应用经济学与数据分析研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对序列数据分布偏移检测难题，提出基于概率流常微分方程与最大均值差异的在线检测方法，可检测任意分布偏移且无需参数假设。
AI 中文摘要
快速增长的一系列序列数据任务，如识别金融市场的趋势反转、自动分割视频和音频记录、从运动传感器检测运动方向变化，若不检测时序数据中的分布偏移则无法完全解决。我们考虑一个序列变化点检测问题，其中条件密度在未知时刻切换，但变化前和变化后的分布均不具有闭式形式。经典似然比统计量不适用于此类场景。在变化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定义确定性双射；变化前观测被映射为标准高斯潜在变量，而经过同一冻结映射处理的变化后观测则偏离该参考。我们采用最大均值差异作为检验统计量，推导其在高斯原假设下各分量的闭式表达式，并确立其作为退化U统计量的渐近分布。随后，我们将Shiryaev–Roberts在线检测程序应用于所得统计量，进行精确阈值校准。该方法可检测任意分布偏移，包括协方差旋转和高阶结构突变，且无需对任一状态做参数假设。
英文摘要
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.
