# Learning MR-Sort Models from Non-Monotone Data

arXiv: https://arxiv.org/abs/2107.09668 · HTML: https://mlsanity.com/paper/2107.09668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 20 Jul 2021.

## Builds on (most cited first, 2 of 2)

- [Monotonic classification: an overview on algorithms, performance measures and data sets](https://mlsanity.com/paper/1811.07155/) (2018)
- [An efficient SAT formulation for learning multiple criteria non-compensatory sorting rules from examples](https://mlsanity.com/paper/1710.10098/) (2017)

## Abstract (arXiv)

The Majority Rule Sorting (MR-Sort) method assigns alternatives evaluated on multiple criteria to one of the predefined ordered categories. The Inverse MR-Sort problem (Inv-MR-Sort) computes MR-Sort parameters that match a dataset. Existing learning algorithms for Inv-MR-Sort consider monotone preferences on criteria. We extend this problem to the case where the preferences on criteria are not necessarily monotone, but possibly single-peaked (or single-valley). We propose a mixed-integer programming based algorithm that learns the preferences on criteria together with the other MR-Sort parameters from the training data. We investigate the performance of the algorithm using numerical experiments and we illustrate its use on a real-world case study.