# Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS

arXiv: https://arxiv.org/abs/2607.18209 · HTML: https://mlsanity.com/paper/2607.18209/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 73 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 30 of 36)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Subspace Identification for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2310.04723/) (2023)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments](https://mlsanity.com/paper/2106.09913/) (2021)
- [Domain adaptation under structural causal models](https://mlsanity.com/paper/2010.15764/) (2020)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [sJIVE: Supervised Joint and Individual Variation Explained](https://mlsanity.com/paper/2102.13278/) (2021)
- [Partial Identifiability for Domain Adaptation](https://mlsanity.com/paper/2306.06510/) (2023)
- [Sufficient Forecasting Using Factor Models](https://mlsanity.com/paper/1505.07414/) (2015)
- [Why Do Probabilistic Clinical Models Fail To Transport Between Sites?](https://mlsanity.com/paper/2311.04787/) (2023)
- [Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors](https://mlsanity.com/paper/1908.01252/) (2019)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Estimating shared subspace with AJIVE: the power and limitation of multiple data matrices](https://mlsanity.com/paper/2501.09336/) (2025)
- [Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices](https://mlsanity.com/paper/2411.17054/) (2024)
- [Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration](https://mlsanity.com/paper/2507.22170/) (2025)
- [Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise](https://mlsanity.com/paper/1806.01094/) (2018)
- [The Causal Structure of Domain Invariant Supervised Representation Learning](https://mlsanity.com/paper/2208.06987/) (2022)
- [Joint and Individual Component Regression](https://mlsanity.com/paper/2209.12388/) (2022)
- [Bayesian Combinatorial Multi-Study Factor Analysis](https://mlsanity.com/paper/2007.12616/) (2020)
- [Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis](https://mlsanity.com/paper/2305.04113/) (2023)
- [Approximate Factor Models with Weaker Loadings](https://mlsanity.com/paper/2109.03773/) (2021)

## Abstract (arXiv)

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.