Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.

翻译：标准共形异常检测在可交换性假设下提供了边际有限样本保证。然而，真实世界数据通常存在分布偏移，因此需要采用加权共形方法来适应局部非平稳性。我们证明这种适应会导致最小可达p值与其稳定性之间的关键权衡。当重要性权重局域化至相关校准实例时，有效样本量会随之减小。这可能使得标准共形p值在有效误差控制方面过于保守，而用于缓解该问题的平滑技术会引入条件方差，可能掩盖异常。我们提出一种连续推断松弛方法，通过连续加权核密度估计将局部适应与尾部分辨率解耦，从而解决这一困境。在将有限样本精确性松弛为渐近有效性的同时，我们的方法消除了蒙特卡洛变异性并恢复了因离散化损失的统计功效。实证评估表明，我们的方法不仅能在离散基线方法零发现的情况下恢复检测能力，还在维持实际边际误差控制的同时，在统计功效上优于标准方法。