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Label-Efficient Monitoring of Classification Models via Stratified Importance Sampling

Lupo Marsigli, Angel Lopez de Haro

TL;DR

This work addresses the challenge of monitoring deployed classifiers under strict labeling budgets and rare defects by formalizing Stratified Importance Sampling (SIS) as a general, non-adaptive framework with finite-sample guarantees. SIS combines stratification to stabilize between-stratum variability with within-stratum importance weighting to focus labels on informative instances, yielding unbiased estimators and strict MSE improvements over both IS and SRS under mild conditions. Theoretical results characterize when SIS yields gains and when it may not, while extensive experiments across tabular and image datasets demonstrate robust, significant variance reductions and practical gains in typical monitoring regimes. SIS provides a principled, lightweight baseline for label-efficient model monitoring that complements adaptive drift-detection approaches and remains robust to proxy noise and suboptimal strata, with adaptive designs offering potential gains at higher budgets. Overall, the framework offers a solid, finite-sample–guaranteed method for reliable post-deployment monitoring under realistic constraints.

Abstract

Monitoring the performance of classification models in production is critical yet challenging due to strict labeling budgets, one-shot batch acquisition of labels and extremely low error rates. We propose a general framework based on Stratified Importance Sampling (SIS) that directly addresses these constraints in model monitoring. While SIS has previously been applied in specialized domains, our theoretical analysis establishes its broad applicability to the monitoring of classification models. Under mild conditions, SIS yields unbiased estimators with strict finite-sample mean squared error (MSE) improvements over both importance sampling (IS) and stratified random sampling (SRS). The framework does not rely on optimally defined proposal distributions or strata: even with noisy proxies and sub-optimal stratification, SIS can improve estimator efficiency compared to IS or SRS individually, though extreme proposal mismatch may limit these gains. Experiments across binary and multiclass tasks demonstrate consistent efficiency improvements under fixed label budgets, underscoring SIS as a principled, label-efficient, and operationally lightweight methodology for post-deployment model monitoring.

Label-Efficient Monitoring of Classification Models via Stratified Importance Sampling

TL;DR

This work addresses the challenge of monitoring deployed classifiers under strict labeling budgets and rare defects by formalizing Stratified Importance Sampling (SIS) as a general, non-adaptive framework with finite-sample guarantees. SIS combines stratification to stabilize between-stratum variability with within-stratum importance weighting to focus labels on informative instances, yielding unbiased estimators and strict MSE improvements over both IS and SRS under mild conditions. Theoretical results characterize when SIS yields gains and when it may not, while extensive experiments across tabular and image datasets demonstrate robust, significant variance reductions and practical gains in typical monitoring regimes. SIS provides a principled, lightweight baseline for label-efficient model monitoring that complements adaptive drift-detection approaches and remains robust to proxy noise and suboptimal strata, with adaptive designs offering potential gains at higher budgets. Overall, the framework offers a solid, finite-sample–guaranteed method for reliable post-deployment monitoring under realistic constraints.

Abstract

Monitoring the performance of classification models in production is critical yet challenging due to strict labeling budgets, one-shot batch acquisition of labels and extremely low error rates. We propose a general framework based on Stratified Importance Sampling (SIS) that directly addresses these constraints in model monitoring. While SIS has previously been applied in specialized domains, our theoretical analysis establishes its broad applicability to the monitoring of classification models. Under mild conditions, SIS yields unbiased estimators with strict finite-sample mean squared error (MSE) improvements over both importance sampling (IS) and stratified random sampling (SRS). The framework does not rely on optimally defined proposal distributions or strata: even with noisy proxies and sub-optimal stratification, SIS can improve estimator efficiency compared to IS or SRS individually, though extreme proposal mismatch may limit these gains. Experiments across binary and multiclass tasks demonstrate consistent efficiency improvements under fixed label budgets, underscoring SIS as a principled, label-efficient, and operationally lightweight methodology for post-deployment model monitoring.
Paper Structure (35 sections, 6 theorems, 44 equations, 1 figure, 10 tables, 1 algorithm)

This paper contains 35 sections, 6 theorems, 44 equations, 1 figure, 10 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARY
  3. METHODS
  4. EXPERIMENTS
  5. Experimental design.
  6. Implementation of strata and proposal distributions.
  7. Efficiency gains from proxy strata and noisy proposal distributions.
  8. Comparison to adaptive approaches.
  9. RELATED WORK
  10. CONCLUSION
  11. BASELINE SAMPLING DESIGNS
  12. PROOFS OF THE EFFICIENCY IMPROVEMENT OF SIS
  13. THEORETICAL PROPERTIES OF SIS ESTIMATOR
  14. Extended Experimental Results
  15. Description of the Datasets
  16. ...and 20 more sections

Key Result

Theorem 1

Consider the task of estimating $\epsilon=\mathbb{E}[Z]$, where $Z=z(X)\in\{0,1\}$. Let the population be partitioned into $P$ strata with population weights $w_j=\mathbb{P}_p(S=j)$, and let $r_j=\mathbb{P}_q(S=j)$ denote the stratum marginals under an Importance Sampling proposal $q$. Within each s and the within–stratum IS second–moment gap Assume: (i) absolute continuity within strata $p_j\ll

Figures (1)

  • Figure 1: Comparison of sampling designs on MNIST and BCW. Lines show mean MSE (log scale) versus sample size; shaded regions indicate 95% confidence bands ($\pm 1.96\,\mathrm{SE}$) across simulations.

Theorems & Definitions (11)

  • Definition 1: Relative Efficiency of two Estimators
  • Theorem 1: Efficiency improvement of the Stratified Importance Sampling estimator against Importance Sampling
  • Theorem 2: Efficiency improvement of the Stratified Importance Sampling estimator against Stratified Random Sampling
  • Theorem 2: Efficiency improvement of the Stratified Importance Sampling estimator against Importance Sampling
  • proof : Proof
  • Theorem 2: Efficiency improvement of the Stratified Importance Sampling estimator against Stratified Random Sampling
  • proof : Proof
  • Proposition 1
  • proof
  • Proposition 2
  • ...and 1 more