Factorizable joint shift revisited

2026-07-08 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Dirk Tasche's paper "Factorizable joint shift revisited" extends the concept of factorizable joint shift (FJS) to general label spaces, encompassing both classification and regression models. It generalizes existing characterizations of FJS and proposes an extension of the expectation maximization (EM) algorithm for estimating target prior class probabilities. The research also re-examines generalized label shift (GLS) within this broader framework, demonstrating that GLS implies FJS even with general label spaces. The paper establishes a comprehensive probabilistic setting for analyzing distribution shift. It details how source and target distributions are linked via Radon-Nikodym derivatives and provides iterative methods for inferring target distribution characteristics when marginals are known or only feature marginals are available.

Key takeaway

For AI scientists developing robust classification or regression models under distribution shift, this work offers a generalized mathematical framework for Factorizable Joint Shift (FJS) and Generalized Label Shift (GLS). You can apply the proposed iterative solution for `psi` to infer target distribution properties when both feature and label marginals are known. Alternatively, use the extended EM algorithm to estimate target label densities from target feature data, enhancing model adaptability.

Key insights

FJS and GLS frameworks are extended to general label spaces, enabling broader application in distribution shift scenarios.

Principles

• FJS can be decomposed into consecutive label and covariate shifts.
• Absolute continuity of target distribution relative to source is a strong but useful assumption.
• Conditional densities given features are homogeneous under FJS.

Method

An iterative approach is proposed to solve a non-linear integral equation for the unknown function `psi` in FJS. A generalized EM algorithm is presented for estimating target label density.

In practice

• Use the iterative method to infer target distribution characteristics when marginals are known.
• Apply the generalized EM algorithm to estimate target label density from target feature data.

Topics

• Distribution Shift
• Factorizable Joint Shift
• Generalized Label Shift
• Domain Adaptation
• Expectation Maximization
• General Label Spaces

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.