Incremental Uncertainty-aware Performance Monitoring with Active Labeling Intervention

TL;DR

This work tackles the problem of monitoring deployed models under gradual distribution shifts without abundant labels. It introduces Incremental Uncertainty-aware Performance Monitoring (IUPM), an optimal-transport–based framework that builds an incremental transition map $\\Psi_t$ to relate current unlabeled data to the initial labeled distribution and produces a predictive distribution $\\hat{P}(Y_t|X_t)$, accompanied by an uncertainty measure. A key theoretical result shows a linear-in-time error bound $|\\mathcal{L}_t - \\hat{\\mathcal{L}}_t^{IUPM}| \le \sum_{i=1}^t L_t \varepsilon_t$, anchored in gradual Lipschitz smoothness, and the paper also introduces an active labeling strategy (UI) that queries the most uncertain samples to reduce uncertainty within a limited labeling budget. Empirically, IUPM outperforms baselines across synthetic, MNIST, ImageNet-c, and real-world temporal shifts, and UI further improves accuracy with substantially fewer labeled examples, highlighting the method’s practical impact for reliable monitoring in dynamic environments.

Abstract

We study the problem of monitoring machine learning models under gradual distribution shifts, where circumstances change slowly over time, often leading to unnoticed yet significant declines in accuracy. To address this, we propose Incremental Uncertainty-aware Performance Monitoring (IUPM), a novel label-free method that estimates performance changes by modeling gradual shifts using optimal transport. In addition, IUPM quantifies the uncertainty in the performance prediction and introduces an active labeling procedure to restore a reliable estimate under a limited labeling budget. Our experiments show that IUPM outperforms existing performance estimation baselines in various gradual shift scenarios and that its uncertainty awareness guides label acquisition more effectively compared to other strategies.

Figures (11)

• Figure 1: Illustration of Incremental Uncertainty-aware Performance Monitoring (IUPM) to estimate performance changes over time using only labels from the initial training distribution. By iteratively linking unlabeled data points using optimal transport couplings $\gamma$ and combining them into an overall transition map $\Psi$, it can anticipate the true model performance under gradual shifts. IUPM also provides an inherent uncertainty measure and an active labeling procedure to efficiently reduce uncertainty and improve estimation reliability under a limited labeling budget.
• Figure 2: Synthetic two-dimensional toy datasets and corresponding shifts indicated by black arrows.
• Figure 3: Performance estimation for an MLP model on the synthetic moons data set for a rotational shift over 100 steps resulting in a total rotation of 200°. Our proposed IUPM approach with and without label intervention clearly yields the highest fidelity for the performance estimation.
• Figure 3: Mean Average Error (MAE) between ground truth and estimated accuracy for a LeNet across three different shifts on the MNIST data set. The table shows the mean across five random seeds, we refer to \ref{['app:D']} for confidence intervals.
• Figure 4: Comparison of sampling strategy using Active Label Intervention on moons data set over 100 steps. All intervention strategies allow keeping the uncertainty below the predefined threshold, however, our proposed Uncertainty Intervention (UI) requires far fewer intervention steps.

Theorems & Definitions (11)

• Definition 1
• Definition 2
• Proposition 1
• Theorem 1
• Corollary 1
• Definition 2
• Proposition 1
• proof
• Theorem 1
• proof