# Learning partially ranked data based on graph regularization

## TL;DR

This paper introduces a graph-regularized EM algorithm for estimating parameters from partially ranked data, effectively handling non-ignorable missing mechanisms with theoretical guarantees and improved accuracy.

## Contribution

It proposes a novel estimation method combining graph regularization with EM to address non-ignorable missing data in partial rankings, reducing modeling bias.

## Key findings

- Estimates perform well under non-ignorable missing mechanisms.
- The method has guaranteed convergence properties.
- Experimental results validate the effectiveness of the approach.

## Abstract

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.