# False membership rate control in mixture models

arXiv: https://arxiv.org/abs/2203.02597 · HTML: https://mlsanity.com/paper/2203.02597/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [On Learning Mixtures of Well-Separated Gaussians](https://mlsanity.com/paper/1710.11592/) (2017)
- [Partial recovery bounds for clustering with the relaxed Kmeans](https://mlsanity.com/paper/1807.07547/) (2018)
- [Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation](https://mlsanity.com/paper/1306.2035/) (2013)
- [Error rate control for classification rules in multiclass mixture models](https://mlsanity.com/paper/2109.14235/) (2021)

## Abstract (arXiv)

The clustering task consists in partitioning elements of a sample into homogeneous groups. Most datasets contain individuals that are ambiguous and intrinsically difficult to attribute to one or another cluster. However, in practical applications, misclassifying individuals is potentially disastrous and should be avoided. To keep the misclassification rate small, one can decide to classify only a part of the sample. In the supervised setting, this approach is well known and referred to as classification with an abstention option. In this paper the approach is revisited in an unsupervised mixture model framework and the purpose is to develop a method that comes with the guarantee that the false membership rate (FMR) does not exceed a pre-defined nominal level α. A plug-in procedure is proposed, for which a theoretical analysis is provided, by quantifying the FMR deviation with respect to the target level α with explicit remainder terms. Bootstrap versions of the procedure are shown to improve the performance in numerical experiments.