stat.MLApr 5, 2026

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

Authors: Prakul Sunil Hiremath

Organizations: Department of Computer Science and Engineering, Visvesvaraya Technological University (VTU), Belagavi, India · Aliens on Earth (AoE) Autonomous Research Group, Belagavi, India

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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.

Figures & tables

DomainRepresentative SystemλH\bm{\lambda_{\mathcal{H}}}τ1/2\bm{\tau_{1/2}}
Ultra-High Latency SensitivityHigh-Frequency / Algorithmic Trading0.500.501.391.39 steps
Network Security & IDSIntrusion Detection (NSL-KDD)0.140.144.954.95 steps
Cyber-Physical & BioRefineryBIOLOOP Industrial Control0.050.0513.8613.86 steps
Epidemiological SurveillancePandemic Onset Detection0.020.0234.6634.66 steps
Seismic Early WarningP-wave / S-wave Discrimination0.010.0169.3169.31 steps
Table 1: The Hiremath Standard Table. Domain-indexed calibration of the Hiremath Decay Constant λH\lambda_{\mathcal{H}} and the corresponding Information Half-Life τ1/2=ln⁡(2)/λH\tau_{1/2}=\ln(2)/\lambda_{\mathcal{H}} . Values reflect the minimum response window within which defensive intervention retains positive expected utility.
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