Problem
Research questions and friction points this paper is trying to address.
Change Detection
Sequential Data
Distributional Shifts
Conditional Density
Change Detection in Probability Flow ODE: Online Testing in Diffusion Latent Spaces
🤖 AI Summary
本文提出了一种基于条件扩散模型和概率流ODE的方法，通过最大均值差异检测时间序列数据中的分布变化，解决了传统方法无法处理的无闭式分布变化检测问题。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Conditional Diffusion Model
Maximum Mean Discrepancy
Online Change Detection
Gaussian Latent Space
Shiryaev--Roberts Procedure
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