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

Thiago Ramos, Alek Fröhlich, Daniel Perazzo, Massimiliano Pontil

Keywords: Distribution Drift, Uncertainty Quantification, Functional Newton Method, Density Ratios, Spectral Decomposition, Conditional Expectation Operators

TL;DR: We propose a stagewise method for learning conditional distributions that detects and adapts to harmful distribution shifts via a spectral density-ratio decomposition

Abstract:

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.

Submission Number: 113