Drift-Aware Uncertainty Quantification via a Functional Spectral-Newton Method

Machine learning models are increasingly deployed in high-risk domains such as healthcare and finance, where uncertainty quantification is essential and distribution shifts can severely degrade predictive performance. However, many existing approaches to shift detection and adaptation address isolated components of the catch–adapt–operate cycle, often without explicitly accounting for predictive uncertainty. In this paper, we introduce a stagewise framework for learning conditional distributions that directly targets harmful changes affecting predictive performance. Our method learns a spectral decomposition of the density ratio $f_{XY}/(f_Xf_Y)$ via alternating functional Newton updates, reminiscent of gradient boosting methods. We also introduce a performance degradation metric for identifying shifts that are harmful and should trigger adaptation. Preliminary experiments on conditional distribution estimation benchmarks with induced shifts suggest that this approach offers a principled path toward robust conditional distribution modeling in high-risk, nonstationary environments.