Summary
This paper introduces ATLAS, a framework for transfer learning in multi-environment latent factor models. High-dimensional covariates are collected from heterogeneous environments whose joint distributions may shift, while auxiliary labels are available only for a subset of environments. The latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Using the invariance principle, the authors prove that invariant and heterogeneous factors can be disentangled under minimal structural conditions. Building on this identifiability result, ATLAS uses invariance-guided alignment to separate aligned invariant factors from unaligned heterogeneous factors, then leverages auxiliary label supervision to extract predictive, invariant, and transferable factors from the unaligned components. The method targets stable low-dimensional representations for interpreting a response Y and robust out-of-sample prediction in latent factor regression settings, achieving near-oracle downstream performance. Authored by Yihong Gu, Katherine Liao, and Tianxi Cai, the work spans math.ST, cs.LG, stat.ME, and stat.ML and is available as arXiv:2607.18209.
Paper Overview
- Field: Machine Learning / Statistics
- Authors: Yihong Gu, Katherine Liao, Tianxi Cai
- Released: 2026-07-20
- arXiv: 2607.18209
- Categories: math.ST, cs.LG, stat.ME, stat.ML
Problem Setting
The paper considers a multi-environment latent factor model where high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in only a subset of them. The joint distribution of covariates may vary across environments, while the latent structure decomposes into:
- Invariant factors: sharing common loadings across environments
- Heterogeneous factors: with environment-specific loadings
Motivated by transfer learning and latent factor regression, the goal is to obtain a stable low-dimensional representation for interpreting a response Y and for robust out-of-sample prediction.
Key Contributions
- Identifiability via invariance: Under minimal structural assumptions, the authors prove that invariant and heterogeneous factors can be decoupled using the invariance principle.
- ATLAS pipeline: ATLAS (Alignment of Transferable Latent factors Across heterogeneous environments using auxiliary labels and invariance) is a unified procedure that:
1. Uses the invariance principle to disentangle aligned invariant factors from unaligned heterogeneous factors.
2. Exploits supervision from auxiliary labels to extract predictive, invariant, and transferable factors from the unaligned heterogeneous factors.Results
ATLAS achieves near-oracle performance for downstream latent factor regression and transferable prediction.Links
- arXiv abstract: https://arxiv.org/abs/2607.18209
*Auto-collected on 2026-07-22.*
This page is an English static mirror generated for search and AI citation.
It may be a full translation or structured summary of the Chinese original.
Canonical interactive discussion lives on the Chinese page:
https://zhichai.net/topic/178447003