# Maximin effects in inhomogeneous large-scale data

arXiv: https://arxiv.org/abs/1406.0596 · HTML: https://mlsanity.com/paper/1406.0596/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2014.

## Built on by (most cited first, 30 of 32)

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- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [Meta-Causal Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2208.10156/) (2022)
- [Algorithmic Bias and Data Bias: Understanding the Relation between Distributionally Robust Optimization and Data Curation](https://mlsanity.com/paper/2106.09467/) (2021)
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- [The Role of Learning Algorithms in Collective Action](https://mlsanity.com/paper/2405.06582/) (2024)
- [Breaking Correlation Shift via Conditional Invariant Regularizer](https://mlsanity.com/paper/2207.06687/) (2022)
- [Minimax Regret Learning for Data with Heterogeneous Subgroups](https://mlsanity.com/paper/2405.01709/) (2024)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [CRoFT: Robust Fine-Tuning with Concurrent Optimization for OOD Generalization and Open-Set OOD Detection](https://mlsanity.com/paper/2405.16417/) (2024)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Distributionally Robust Learning for Multi-source Unsupervised Domain Adaptation](https://mlsanity.com/paper/2309.02211/) (2023)
- [Class Distribution Shifts in Zero-Shot Learning: Learning Robust Representations](https://mlsanity.com/paper/2311.18575/) (2023)
- [Distributionally Robust Classification for Multi-source Unsupervised Domain Adaptation](https://mlsanity.com/paper/2601.21315/) (2026)
- [Maximum Risk Minimization with Random Forests](https://mlsanity.com/paper/2512.10445/) (2025)
- [Counterfactual Generation Under Confounding](https://mlsanity.com/paper/2210.12368/) (2022)
- [Multi-dimensional domain generalization with low-rank structures](https://mlsanity.com/paper/2309.09555/) (2023)
- [Boosted Control Functions: Distribution generalization and invariance in confounded models](https://mlsanity.com/paper/2310.05805/) (2023)
- [Invariant Subspace Decomposition](https://mlsanity.com/paper/2404.09962/) (2024)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [On Counterfactual Data Augmentation Under Confounding](https://mlsanity.com/paper/2305.18183/) (2023)
- [DICS: Find Domain-Invariant and Class-Specific Features for Out-of-Distribution Generalization](https://mlsanity.com/paper/2409.08557/) (2024)
- [CTC-DRO: Robust Optimization for Reducing Language Disparities in Speech Recognition](https://mlsanity.com/paper/2502.01777/) (2025)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [Delta Energy: Optimizing Energy Change During Vision-Language Alignment Improves both OOD Detection and OOD Generalization](https://mlsanity.com/paper/2510.11296/) (2025)
- [Adversarial Drift-Aware Predictive Transfer: Toward Durable Clinical AI](https://mlsanity.com/paper/2601.11860/) (2026)
- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)
- [Maximin Relative Improvement: Fair Learning as a Bargaining Problem](https://mlsanity.com/paper/2602.04155/) (2026)
- [Anti-causal domain generalization: Leveraging unlabeled data](https://mlsanity.com/paper/2602.17187/) (2026)
- [Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes](https://mlsanity.com/paper/2603.27114/) (2026)

## Abstract (arXiv)

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary. If we just ask for a model estimator that shows good predictive properties for all regimes of the data, then we are aiming for a simple linear model that is reliable for all possible subsets of the data. We propose the concept of "maximin effects" and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure. Under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators, making computations on large-scale data feasible. Empirical examples complement the novel methodology and theory.