# Anchor PCA

arXiv: https://arxiv.org/abs/2606.06233 · HTML: https://mlsanity.com/paper/2606.06233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Provable Domain Generalization via Invariant-Feature Subspace Recovery](https://mlsanity.com/paper/2201.12919/) (2022)
- [Minimax Regret Optimization for Robust Machine Learning under Distribution Shift](https://mlsanity.com/paper/2202.05436/) (2022)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Distributional Principal Autoencoders](https://mlsanity.com/paper/2404.13649/) (2024)
- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)
- [Invariant Subspace Decomposition](https://mlsanity.com/paper/2404.09962/) (2024)
- [Unsupervised Representation Learning - an Invariant Risk Minimization Perspective](https://mlsanity.com/paper/2505.12506/) (2025)
- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)

## Built on by (most cited first, 1 of 1)

- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026)

## Abstract (arXiv)

Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data. However, this approach can focus on spurious directions that exhibit high variation in only a few domains. To find a robust embedding that still explains most variance in unseen but similar domains, we propose instead to focus on shared directions of variation. To this end, we introduce Anchor PCA which trades off overall explained variance with agreement between the shared and domain-specific low-rank embeddings. Anchor PCA amounts to PCA on a modified target matrix and thus can be solved efficiently. Moreover, we show that Anchor PCA recovers a maximal invariant subspace and admits a minimax reconstruction interpretation under bounded domain-specific covariance inflations. On simulated and real-world gas sensor data with temporal drift, we demonstrate, respectively, that Anchor PCA recovers the maximally invariant subspace and yields embeddings that explain more variance on unseen domains than the pooling baseline and a worst-case alternative. Taken together, these findings establish Anchor PCA as a promising approach to robust unsupervised dimension reduction from multi-domain data.