Bet on Features: Anytime-Valid and Feature-Aware Auditing of Conditional Quantile Forecasters

2026-07-13

AI Summary

This work addresses the challenge that existing calibration tests for conditional quantile predictors struggle to handle distributional shifts and discrepancies in information sets, lacking feature-aware, continuous monitoring capabilities. The authors propose a distribution-free, game-theoretic sequential auditing framework that formally defines conditional quantile calibration under varying feature information sets—a notion not previously established—and provides finite-time detection guarantees without requiring independent and identically distributed data. By integrating contextual linear betting strategies with nonparametric e-processes, the method enables interpretable, feature-level calibration audits. Empirical evaluations demonstrate that the framework effectively detects significant miscalibration in state-of-the-art time series models, such as Chronos-2, across critical features.

Abstract

Black-box conditional quantile forecasts are widely used for sequential decisions under asymmetric costs, such as inventory planning in supply chain management. Once deployed, such forecasters must be monitored continuously as data streams drift and regimes change; this invalidates standard, fixed-horizon backtests for calibration. Further, existing backtests do not take into account that the notion of calibration is, in fact, information-dependent: forecasts can look calibrated to an auditor with coarse information while being miscalibrated to an auditor with richer information. We develop a distribution-free and game-theoretic testing framework for continuously auditing black-box conditional quantile forecasters with non-i.i.d. losses, such that the resulting evidence process is powerful against predictably chosen alternatives specified by the features available to the auditor. We first formalize notions of conditional quantile calibration when different sets of features are available to the auditor, establishing that the coarseness of the auditor's information set determines the hardness of the testing problem. We then identify the sets of alternatives for which the auditor can achieve power, and focusing on contextual bets linear in the features, we derive finite-time detection guarantees for such alternatives, all without an i.i.d. assumption. The resulting evidence processes are interpretable at the feature level, as they quantify fine-grained, "feature-aware" evidence for miscalibration. We empirically validate these methods on simulated and real data, finding that a popular time series forecaster (Chronos-2) is highly miscalibrated w.r.t. multiple relevant features.

Problem

• conditional quantile forecasting
• calibration auditing
• feature-aware testing
• non-i.i.d. data
• information-dependent calibration

Innovation

• conditional quantile calibration
• anytime-valid testing
• feature-aware auditing
• game-theoretic testing
• non-i.i.d. sequential monitoring