Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS

2026-07-20

AI Summary

Identifying latent factors that are stable and transferable across distributionally heterogeneous environments is a key challenge for robust cross-environment prediction. This work proposes ATLAS, the first method to strictly disentangle invariant from environment-specific factors via structural conditioning in heterogeneous settings with partially available auxiliary labels, while unifying treatment of both labeled and unlabeled scenarios for transfer prediction. ATLAS integrates invariance-guided latent alignment, exploitation of auxiliary supervision signals, and low-dimensional latent factor regression, and comes with non-asymptotic theoretical guarantees on prediction error. Experiments demonstrate that ATLAS nearly perfectly recovers the true invariant factors and achieves oracle-level regression performance by enabling full latent signal transfer to novel environments.

Abstract

This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Such a model is motivated by transfer learning and latent factor regression, where one seeks stable low-dimensional representations for both interpretation and robust out-of-sample prediction of the response $Y$. Leveraging the invariance principle, we show that the invariant and heterogeneous factors are disentangled under a minimal structural condition. Based on this, we propose ATLAS, an Auxiliary-label and invariance-guided Transfer via Latent Alignment across heterogeneous environmentS. ATLAS is a unified procedure that leverages the invariance principle to separate aligned invariant and unaligned heterogeneous factors, and further exploits supervision from auxiliary labels to extract prediction-invariant and transferable factors from those unaligned heterogeneous factors. ATLAS yields near-oracle performance for downstream latent factor regression, enables transferable prediction in new environments through the full latent signal when auxiliary labels are available, and reduces to robust invariant-factor-only prediction otherwise. We establish sharp non-asymptotic error bounds for recovering invariant and heterogeneous factors, identifying all the response-invariant factors, and estimating the invariant signal in $Y$.

Problem

• invariant factors
• transferable representation
• heterogeneous environments
• latent factor model
• multi-environment learning

Innovation

• invariant representation
• transfer learning
• latent factor disentanglement
• heterogeneous environments
• auxiliary labels