# Learning partially ranked data based on graph regularization

arXiv: https://arxiv.org/abs/1902.10963 · HTML: https://mlsanity.com/paper/1902.10963/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms](https://mlsanity.com/paper/2304.09872/) (2023)
- [Comparing Machine Learning Algorithms by Union-Free Generic Depth](https://mlsanity.com/paper/2312.12839/) (2023)

## Abstract (arXiv)

Ranked data appear in many different applications, including voting and consumer surveys. There often exhibits a situation in which data are partially ranked. Partially ranked data is thought of as missing data. This paper addresses parameter estimation for partially ranked data under a (possibly) non-ignorable missing mechanism. We propose estimators for both complete rankings and missing mechanisms together with a simple estimation procedure. Our estimation procedure leverages a graph regularization in conjunction with the Expectation-Maximization algorithm. Our estimation procedure is theoretically guaranteed to have the convergence properties. We reduce a modeling bias by allowing a non-ignorable missing mechanism. In addition, we avoid the inherent complexity within a non-ignorable missing mechanism by introducing a graph regularization. The experimental results demonstrate that the proposed estimators work well under non-ignorable missing mechanisms.