# Finding Most Influential Sets

arXiv: https://arxiv.org/abs/2606.05919 · HTML: https://mlsanity.com/paper/2606.05919/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 4 Jun 2026.

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

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [MPNet: Masked and Permuted Pre-training for Language Understanding](https://mlsanity.com/paper/2004.09297/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [On Second-Order Group Influence Functions for Black-Box Predictions](https://mlsanity.com/paper/1911.00418/) (2019)
- [Poisoning Attacks on LLMs Require a Near-constant Number of Poison Samples](https://mlsanity.com/paper/2510.07192/) (2025)
- [Most Influential Subset Selection: Challenges, Promises, and Beyond](https://mlsanity.com/paper/2409.18153/) (2024)
- [An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?](https://mlsanity.com/paper/2011.14999/) (2020)
- [Data Cleaning and Machine Learning: A Systematic Literature Review](https://mlsanity.com/paper/2310.01765/) (2023)
- [Approximations to worst-case data dropping: unmasking failure modes](https://mlsanity.com/paper/2408.09008/) (2024)
- [Provably Auditing Ordinary Least Squares in Low Dimensions](https://mlsanity.com/paper/2205.14284/) (2022)
- [Towards Practical Robustness Auditing for Linear Regression](https://mlsanity.com/paper/2307.16315/) (2023)
- [Robustness Auditing for Linear Regression: To Singularity and Beyond](https://mlsanity.com/paper/2410.07916/) (2024)
- [Testing Most Influential Sets](https://mlsanity.com/paper/2510.20372/) (2025)

## Abstract (arXiv)

Identifying most influential sets (MIS) - size-k subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over binomnk subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-k problems. Dinkelbach's method yields an algorithm with O(n) cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.