# Causally Regularized Learning with Agnostic Data Selection Bias

arXiv: https://arxiv.org/abs/1708.06656 · HTML: https://mlsanity.com/paper/1708.06656/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

## Built on by (most cited first, 29 of 29)

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- [Harnessing Out-Of-Distribution Examples via Augmenting Content and Style](https://mlsanity.com/paper/2207.03162/) (2022)
- [Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shift](https://mlsanity.com/paper/2211.02843/) (2022)
- [Analysis and Applications of Class-wise Robustness in Adversarial Training](https://mlsanity.com/paper/2105.14240/) (2021)
- [Debiased Graph Neural Networks with Agnostic Label Selection Bias](https://mlsanity.com/paper/2201.07708/) (2022)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [Contrastive ACE: Domain Generalization Through Alignment of Causal Mechanisms](https://mlsanity.com/paper/2106.00925/) (2021)
- [A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization](https://mlsanity.com/paper/2111.02355/) (2021)
- [Object-Aware Regularization for Addressing Causal Confusion in Imitation Learning](https://mlsanity.com/paper/2110.14118/) (2021)
- [Distributionally Robust Learning with Stable Adversarial Training](https://mlsanity.com/paper/2106.15791/) (2021)
- [Meta-Causal Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2208.10156/) (2022)
- [Stable Learning via Sparse Variable Independence](https://mlsanity.com/paper/2212.00992/) (2022)
- [Effective Causal Discovery under Identifiable Heteroscedastic Noise Model](https://mlsanity.com/paper/2312.12844/) (2023)
- [Exploiting Personalized Invariance for Better Out-of-distribution Generalization in Federated Learning](https://mlsanity.com/paper/2211.11243/) (2022)
- [ConfounderGAN: Protecting Image Data Privacy with Causal Confounder](https://mlsanity.com/paper/2212.01767/) (2022)
- [GABRIL: Gaze-Based Regularization for Mitigating Causal Confusion in Imitation Learning](https://mlsanity.com/paper/2507.19647/) (2025)
- [Causal Feature Selection for Responsible Machine Learning](https://mlsanity.com/paper/2402.02696/) (2024)
- [DCAST: Diverse Class-Aware Self-Training Mitigates Selection Bias for Fairer Learning](https://mlsanity.com/paper/2409.20126/) (2024)
- [Stable Heterogeneous Treatment Effect Estimation across Out-of-Distribution Populations](https://mlsanity.com/paper/2407.03082/) (2024)
- [Identifying Auxiliary or Adversarial Tasks Using Necessary Condition Analysis for Adversarial Multi-task Video Understanding](https://mlsanity.com/paper/2208.10077/) (2022)
- [Prediction with Incomplete Data under Agnostic Mask Distribution Shift](https://mlsanity.com/paper/2305.11197/) (2023)
- [Causal Perception Inspired Representation Learning for Trustworthy Image Quality Assessment](https://mlsanity.com/paper/2404.19567/) (2024)
- [Beyond Correlation: Causal Multi-View Unsupervised Feature Selection Learning](https://mlsanity.com/paper/2509.13763/) (2025)
- [Can We Trust In-Distribution Success? Locked Evaluation Reveals Transfer Failure and Sampling-Depth Entanglement in CRISPRi Perturbation Prediction](https://mlsanity.com/paper/2608.00152/) (2026)
- [Decoupled Causal Discovery](https://mlsanity.com/paper/2609.23535/) (2026)

## Abstract (arXiv)

Most of previous machine learning algorithms are proposed based on the i.i.d. hypothesis. However, this ideal assumption is often violated in real applications, where selection bias may arise between training and testing process. Moreover, in many scenarios, the testing data is not even available during the training process, which makes the traditional methods like transfer learning infeasible due to their need on prior of test distribution. Therefore, how to address the agnostic selection bias for robust model learning is of paramount importance for both academic research and real applications. In this paper, under the assumption that causal relationships among variables are robust across domains, we incorporate causal technique into predictive modeling and propose a novel Causally Regularized Logistic Regression (CRLR) algorithm by jointly optimize global confounder balancing and weighted logistic regression. Global confounder balancing helps to identify causal features, whose causal effect on outcome are stable across domains, then performing logistic regression on those causal features constructs a robust predictive model against the agnostic bias. To validate the effectiveness of our CRLR algorithm, we conduct comprehensive experiments on both synthetic and real world datasets. Experimental results clearly demonstrate that our CRLR algorithm outperforms the state-of-the-art methods, and the interpretability of our method can be fully depicted by the feature visualization.