arXiv:2604.04993stat.MLcs.CR2026-04

提出新评估标准HED,精准衡量异常检测的提前时间价值。

The Hiremath Early Detection (HED) Score: A Measure-Theoretic Evaluation Standard for Temporal Intelligence

  • 用指数衰减核融合后验概率流,量化检测时机与准确性。
  • 在NSL-KDD数据集上比随机森林提升388.8%,显著优于传统AUC。
  • 适合安全监控、疫情预警等需快速响应的实时系统场景。

我们提出测量论基础的猎马斯早期检测(HED)评分,用于评估非平稳随机过程在突发状态转换下信息的时间价值。现有评估范式如ROC/AUC对检测延迟不敏感,无法区分t+1与t+τ的检测,这在网络安全、算法监控和流行病学中是根本缺陷。HED评分通过在状态转移起点开始,对后验概率流施加基线无关的指数衰减核,生成一个同时包含检测精度、提前量和事前校准质量的标量。我们证明了该评分满足三项公理:(A1) 时间单调性,(A2) 事前偏倚不变性,(A3) 敏感性可分解性。此外,其参数族由猎马斯衰减常数(λ_H)定义,对应领域校准形成猎马斯标准表。作为实证模型,我们提出PARD-SSM(基于分数阶随机微分方程与切换线性动态系统的异常与状态检测),在NSL-KDD数据集上获得0.0643的HED评分,较随机森林基线(0.0132)提升388.8%,经块重抽样验证具有统计显著性(p < 0.001)。建议以HED评分取代传统ROC/AUC。

原文摘要 · Abstract (English)

We introduce the Hiremath Early Detection (HED) Score, a principled, measure-theoretic evaluation criterion for quantifying the time-value of information in systems operating over non-stationary stochastic processes subject to abrupt regime transitions. Existing evaluation paradigms, chiefly the ROC/AUC framework and its downstream variants, are temporally agnostic: they assign identical credit to a detection at t + 1 and a detection at t + tau for arbitrarily large tau. This indifference to latency is a fundamental inadequacy in time-critical domains including cyber-physical security, algorithmic surveillance, and epidemiological monitoring. The HED Score resolves this by integrating a baseline-neutral, exponentially decaying kernel over the posterior probability stream of a target regime, beginning precisely at the onset of the regime shift. The resulting scalar simultaneously encodes detection acuity, temporal lead, and pre-transition calibration quality. We prove that the HED Score satisfies three axiomatic requirements: (A1) Temporal Monotonicity, (A2) Invariance to Pre-Attack Bias, and (A3) Sensitivity Decomposability. We further demonstrate that the HED Score admits a natural parametric family indexed by the Hiremath Decay Constant (lambda_H), whose domain-specific calibration constitutes the Hiremath Standard Table. As an empirical vehicle, we present PARD-SSM (Probabilistic Anomaly and Regime Detection via Switching State-Space Models), which couples fractional Stochastic Differential Equations (fSDEs) with a Switching Linear Dynamical System (S-LDS) inference backend. On the NSL-KDD benchmark, PARD-SSM achieves a HED Score of 0.0643, representing a 388.8 percent improvement over a Random Forest baseline (0.0132), with statistical significance confirmed via block-bootstrap resampling (p < 0.001). We propose the HED Score as the successor evaluation standard to ROC/AUC.

早期检测时间价值状态转换评估标准

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