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

TL;DR

The paper introduces the HED Score, a measure-theoretic evaluation criterion for quantifying the timeliness and accuracy of regime detection in non-stationary stochastic systems, addressing limitations of existing methods.

Contribution

It proposes the HED Score, a new evaluation standard that incorporates detection latency and calibration, with theoretical properties and empirical validation on anomaly detection benchmarks.

Findings

HED Score satisfies key axiomatic properties for temporal detection evaluation.

PARD-SSM achieves a 388.8% improvement over baseline in HED Score on NSL-KDD.

HED Score is proposed as a superior successor to ROC/AUC for time-critical detection tasks.

Abstract

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.