提出一种可随时验证的在线数据分布变化检测与稳定适应方法
Technical note on Sequential Test-Time Adaptation via Martingale-Driven Fisher Prompting
- 用指数鞅和维尔不等式实现任意时刻的误报控制
- 检测延迟受分布偏移程度影响，理论上限为O(log(1/δ)/Γ)
- 通过Fisher预处理使提示参数更新保持几何稳定性
我们提出了M-FISHER的理论框架，用于流式数据中顺序分布偏移的检测与稳定适应。检测方面，从非符合性得分构建指数鞅，利用维尔不等式获得时间一致的误报控制，确保在任意停止时刻均具统计有效性。在持续偏移下，我们进一步将期望检测延迟界定为O(log(1/δ)/Γ)，其中Γ反映偏移后信息增益，将检测效率与分布差异关联。在适应方面，我们证明了提示参数的Fisher预处理更新等价于分布流形上的自然梯度下降，实现局部最优更新，最小化KL散度的同时保持稳定性和参数化不变性。这些结果共同确立了M-FISHER在协变量偏移下的鲁棒、任意时刻有效的检测与几何稳定适应的理论基础。
原文摘要 · Abstract (English)
We present a theoretical framework for M-FISHER, a method for sequential distribution shift detection and stable adaptation in streaming data. For detection, we construct an exponential martingale from non-conformity scores and apply Ville's inequality to obtain time-uniform guarantees on false alarm control, ensuring statistical validity at any stopping time. Under sustained shifts, we further bound the expected detection delay as $\mathcal{O}(\log(1/δ)/Γ)$, where $Γ$ reflects the post-shift information gain, thereby linking detection efficiency to distributional divergence. For adaptation, we show that Fisher-preconditioned updates of prompt parameters implement natural gradient descent on the distributional manifold, yielding locally optimal updates that minimize KL divergence while preserving stability and parameterization invariance. Together, these results establish M-FISHER as a principled approach for robust, anytime-valid detection and geometrically stable adaptation in sequential decision-making under covariate shift.
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