Blind-Spot Mass: A Good-Turing Framework for Quantifying Deployment Coverage Risk in Machine Learning Systems

Biplab Pal; Santanu Bhattacharya; Madanjit Singh

cs.LGApr 6, 2026

Blind-Spot Mass: A Good-Turing Framework for Quantifying Deployment Coverage Risk in Machine Learning Systems

Authors: Biplab Pal, Santanu Bhattacharya, Madanjit Singh

Organizations: CARDS (Center for Real-Time Distributed Sensing and Autonomy), University of Maryland, Baltimore County (UMBC) · Massachusetts Institute of Technology · Ambient Scientific Inc.

Abstract

Blind-spot mass is a Good-Turing framework for quantifying deployment coverage risk in machine learning. In modern ML systems, operational state distributions are often heavy-tailed, implying that a long tail of valid but rare states is structurally under-supported in finite training and evaluation data. This creates a form of 'coverage blindness': models can appear accurate on standard test sets yet remain unreliable across large regions of the deployment state space. We propose blind-spot mass B_n(tau), a deployment metric estimating the total probability mass assigned to states whose empirical support falls below a threshold tau. B_n(tau) is computed using Good-Turing unseen-species estimation and yields a principled estimate of how much of the operational distribution lies in reliability-critical, under-supported regimes. We further derive a coverage-imposed accuracy ceiling, decomposing overall performance into supported and blind components and separating capacity limits from data limits. We validate the framework in wearable human activity recognition (HAR) using wrist-worn inertial data. We then replicate the same analysis in the MIMIC-IV hospital database with 275 admissions, where the blind-spot mass curve converges to the same 95% at tau = 5 across clinical state abstractions. This replication across structurally independent domains - differing in modality, feature space, label space, and application - shows that blind-spot mass is a general ML methodology for quantifying combinatorial coverage risk, not an application-specific artifact. Blind-spot decomposition identifies which activities or clinical regimes dominate risk, providing actionable guidance for industrial practitioners on targeted data collection, normalization/renormalization, and physics- or domain-informed constraints for safer deployment.

Figures & tables

Figure 1: Conceptual illustration of blind-spot mass under finite sampling. States are ordered by operational probability $p(x)$ (heavy-tailed). A finite sample of size $n$ yields empirical supports $N_{n}(x)$ ; blind-spot mass $B_{n}(\tau)$ corresponds to the total probability of states whose support falls below a threshold $\tau$ .

Panel of Figure 2 — Figure 2: Activity-level window counts (5 s windows) in (a) the in-house dataset and (b) the PAMAP2 benchmark (subjects 101+105). PAMAP2 activity mapping follows the dataset documentation Reiss and Stricker (2012a) ; Reiss and Stricker (2012b) .

Panel of Figure 3 — Figure 3: Per-class accuracy with 95% confidence intervals. (a) In-house dataset (5 test windows/class). (b) PAMAP2 dataset: Wilson 95% intervals; per-class test support ranges from 15 to 133 windows (median 26.5) across hand, chest, and ankle placements.

Panel of Figure 4 — Figure 4: Estimated blind-spot mass $\widehat{B}_{n}(\tau)$ versus support threshold $\tau$ . (a) In-house dataset under activity-only states $x=a$ . (b) PAMAP2 under refined operational abstractions: $x=a$ ( $K_{\mathrm{eff}}=14$ ), $x=(a,p)$ ( $K_{\mathrm{eff}}=44$ ), and $x=(a,p,e)$ ( $K_{\mathrm{eff}}=78$ ).

Figure 5: Cross-domain replication of blind-spot mass curves. We compare a deployment-refined operational abstraction for in-house HAR windows against an admission-level clinical state abstraction on the MIMIC-IV Demo dataset (275 admissions). Both curves converge to

\widehat{B}_{n}(5)\approx 0.95

, illustrating that coverage blindness arises from heavy-tailed, combinatorial state spaces across domains.

Panel of Figure 6 — Figure 6: Coverage-imposed accuracy ceiling versus $\tau$ , overlaid with $\widehat{B}_{n}(\tau)$ .

Panel of Figure 7 — Figure 7: Decomposition of blind-spot mass at fixed $\tau$ . (a) In-house dataset: per-activity contributions at $\tau=150$ . (b) PAMAP2: top composite-state contributions at $\tau=20$ for $x=(a,p,e)$ (activity $a$ , tilt-bin $p$ , energy-bin $e$ ).

State $x$	$N_{n}(x)$	$\hat{P}(x)$	$w(x)$	Contribution
Walking	307	0.183	0.2	0.000
Stairs up	134	0.080	0.6	0.048
Stairs down	144	0.086	0.6	0.052
Front fall	122	0.073	1.0	0.073
Backward fall	122	0.073	1.0	0.073

Table 1: Illustrative risk-weighted blindness example (in-house dataset;

\tau=150

). Risk weights are illustrative and domain-dependent.

Available Guardrails: Certifying Selective Prediction across ML Systems
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Rivian and Volkswagen Group Technologies · Stony Brook University · Westlake University
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Sep 18, 2026J/K move · Enter open · S save

Available Guardrails: Certifying Selective Prediction across ML Systems

Parivesh Priye, Yufeng Wang, Haibin Ling, Michael Chaykowsky

Rivian and Volkswagen Group Technologies · Stony Brook University · Westlake University

Selective Prediction Language Model Safety Evaluation

Open paper AskPDF arXiv

A selective predictor acts as a safety gate: it returns an output only when the prediction appears sufficiently trustworthy. Deployments increasingly require this reliability to be certified at a target precision for every reporting unit of interest, such as a tool, policy label, or patient subgroup. The main difficulty is often not whether a granted certificate is valid, but whether finite calibration data can produce one at all. As the gate becomes safer or more fine-grained, some units may receive too little evidence to certify. We make this notion of availability computable through classical exact-binomial inversion and formulate reporting-partition selection, under a fixed group order, as a dynamic program that exposes the trade-off among safety, granularity, and served traffic. The resulting frontier reveals a large population opportunity that finite-sample estimation nearly erases: a truth-informed planner gains

0.157

mean coverage over support balancing, whereas a naive estimator recovers only

0.005

, making recovery from finite data the central challenge. Constructing candidate partitions on one planning split and selecting among them on another recovers part of this gap, improving mean coverage over support balancing by

0.060

, with the direction reproduced in

59

60

model effects across three intent-routing datasets and two architectures. A complementary validity-preserving lever, reallocating the familywise error budget across reporting units, recovers additional coverage both with population quantities and noisy estimates. The same frontier recurs, with predictor-specific ceilings, across LLM tool-calling, content moderation, lesion classification, and recommendation. Certified availability is therefore a plannable deployment resource that determines when a safety gate can be certified, at what granularity, and over how much traffic.

Abstract

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