# Composite Marginal Likelihood Methods for Random Utility Models

arXiv: https://arxiv.org/abs/1806.01426 · HTML: https://mlsanity.com/paper/1806.01426/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2018.

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

- [On the identifiability of mixtures of ranking models](https://mlsanity.com/paper/2201.13132/) (2022)
- [Efficient and Accurate Learning of Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/2302.05343/) (2023)

## Abstract (arXiv)

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computational efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.