# Understanding Fixed Predictions via Confined Regions

arXiv: https://arxiv.org/abs/2502.16380 · HTML: https://mlsanity.com/paper/2502.16380/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 22 Feb 2025.

## Builds on (most cited first, 27 of 27)

- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Concept Bottleneck Large Language Models](https://mlsanity.com/paper/2412.07992/) (2024)
- [Algorithmic Recourse in the Wild: Understanding the Impact of Data and Model Shifts](https://mlsanity.com/paper/2012.11788/) (2020)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [Algorithmic Collective Action in Machine Learning](https://mlsanity.com/paper/2302.04262/) (2023)
- [GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations](https://mlsanity.com/paper/2305.17021/) (2023)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Interpretable Clustering via Multi-Polytope Machines](https://mlsanity.com/paper/2112.05653/) (2021)
- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [Endogenous Macrodynamics in Algorithmic Recourse](https://mlsanity.com/paper/2308.08187/) (2023)
- [On the Actionability of Outcome Prediction](https://mlsanity.com/paper/2309.04470/) (2023)
- [Generating collective counterfactual explanations in score-based classification via mathematical optimization](https://mlsanity.com/paper/2310.12822/) (2023)
- [Cluster Explanation via Polyhedral Descriptions](https://mlsanity.com/paper/2210.08798/) (2022)
- [Prediction without Preclusion: Recourse Verification with Reachable Sets](https://mlsanity.com/paper/2308.12820/) (2023)
- [Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles](https://mlsanity.com/paper/2205.14116/) (2022)
- [One-for-many Counterfactual Explanations by Column Generation](https://mlsanity.com/paper/2402.09473/) (2024)

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

- [Responsiveness Verification: Will Predictions Change? How Much? How Often?](https://mlsanity.com/paper/2507.02169/) (2025)

## Abstract (arXiv)

Machine learning models can assign fixed predictions that preclude individuals from changing their outcome. Existing approaches to audit fixed predictions do so on a pointwise basis, which requires access to an existing dataset of individuals and may fail to anticipate fixed predictions in out-of-sample data. This work presents a new paradigm to identify fixed predictions by finding confined regions of the feature space in which all individuals receive fixed predictions. This paradigm enables the certification of recourse for out-of-sample data, works in settings without representative datasets, and provides interpretable descriptions of individuals with fixed predictions. We develop a fast method to discover confined regions for linear classifiers using mixed-integer quadratically constrained programming. We conduct a comprehensive empirical study of confined regions across diverse applications. Our results highlight that existing pointwise verification methods fail to anticipate future individuals with fixed predictions, while our method both identifies them and provides an interpretable description.