# Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection

arXiv: https://arxiv.org/abs/2408.02060 · HTML: https://mlsanity.com/paper/2408.02060/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2024.

## Built on by (most cited first, 8 of 8)

- [Stabilizing black-box model selection with the inflated argmax](https://mlsanity.com/paper/2410.18268/) (2024)
- [Locally minimax optimal confidence sets for the best model](https://mlsanity.com/paper/2503.21639/) (2025)
- [Throwing Vines at the Wall: Structure Learning via Random Search](https://mlsanity.com/paper/2510.20035/) (2025)
- [On the Precise Asymptotics of Universal Inference](https://mlsanity.com/paper/2503.14717/) (2025)
- [Reliable Selection of Heterogeneous Treatment Effect Estimators](https://mlsanity.com/paper/2511.18464/) (2025)
- [Hierarchical Clustering With Confidence](https://mlsanity.com/paper/2512.06522/) (2025)
- [Sequential Confidence Sets for Coverage-Constrained Conformal Model Selection](https://mlsanity.com/paper/2609.28522/) (2026)
- [Prequential E-Values for Selected-GP Near-Optimality Certificates](https://mlsanity.com/paper/2609.39123/) (2026)

## Abstract (arXiv)

We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically normal test statistic, even in high-dimensional settings and with potentially many ties in the population mean vector, by integrating concepts and tools from cross-validation and differential privacy. The key technical ingredient is a central limit theorem for globally dependent data. We also propose practical ways to select the tuning parameter that adapts to the signal landscape. Numerical experiments and data examples demonstrate the ability of the proposed method to achieve a favorable bias-variance trade-off in practical scenarios.