需要多少后验样本？自适应感知的校准停止
How Many Posterior Samples? Calibrated Stopping for Adaptive Sensing
- Mitsubishi Electric R&D Centre Europe（三菱电机欧洲研发中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对自适应感知中的停止问题，本文校准固定样本和序贯规则以控制错误声明概率，并证明截断可节省高达62%的后验样本，序贯停止在匹配工作点下成本最低。
AI中文摘要：
在面向分类的自适应感知中，后验样本刻画了当前测量状态下的不确定性，并可发挥两个作用：它们可以指导下一个感知方向，同时它们的类别标签为候选类别提供投票，并决定是否应继续感知。我们专注于停止层，该层将这些投票转化为声明，而不修改后验采样器或感知方向。一个自然的即插即用规则在观察到的投票份额超过阈值时进行声明。我们表明，该阈值本身并不是置信度保证：当底层投票质量等于阈值时，即插即用规则大约有一半的时间会进行声明。作为替代方案，我们将固定样本规则和有限时域序贯规则校准到规定的错误声明概率，并研究精确截断，即在固定池规则最终裁决被迫确定时停止该规则。然后，我们推导出一轮声明概率如何决定沿感知路径的后验样本成本和分类精度。在带有DDRM和固定PCA引导探测序列的MNIST上，截断节省了高达62%的后验样本。在匹配的工作点下评估的规则中，序贯停止降低成本最多。在高精度下，相同的序贯规则可以用更多的后验样本换取更少的测量次数。
英文摘要：
In classification-oriented adaptive sensing, posterior samples characterize uncertainty at the current measurement state and can serve two roles: they may guide the next sensing direction, while their class labels provide votes for the candidate classes and determine whether sensing should continue. We focus on the stopping layer that turns these votes into a declaration, without modifying the posterior sampler or sensing directions. A natural plug-in rule declares when the observed vote share exceeds a threshold. We show that this threshold is not itself a confidence guarantee: when the underlying vote mass equals the threshold, the plug-in rule declares about half the time. As alternatives, we calibrate a fixed-sample rule and a finite-horizon sequential rule to a prescribed false-declaration probability, and study exact curtailment, which stops a fixed-pool rule once its final verdict is forced. We then derive how one-round declaration probabilities determine posterior-sample cost and classification accuracy along a sensing path. On MNIST with DDRM and a fixed PCA-guided probe sequence, curtailment saves up to 62% of posterior samples. Among the evaluated rules at matched operating points, sequential stopping reduces the cost the most. At a high accuracy, that same sequential rule can trade more posterior samples for fewer measurements.
