# Fast Learning of MNL Model from General Partial Rankings with Application to Network Formation Modeling

arXiv: https://arxiv.org/abs/2112.15575 · HTML: https://mlsanity.com/paper/2112.15575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences](https://mlsanity.com/paper/1609.00978/) (2016)
- [Learning Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/1603.07323/) (2016)
- [Predicting Choice with Set-Dependent Aggregation](https://mlsanity.com/paper/1906.06365/) (2019)
- [Data-driven Rank Breaking for Efficient Rank Aggregation](https://mlsanity.com/paper/1601.05495/) (2016)
- [Learning Interpretable Feature Context Effects in Discrete Choice](https://mlsanity.com/paper/2009.03417/) (2020)
- [Choosing to Grow a Graph: Modeling Network Formation as Discrete Choice](https://mlsanity.com/paper/1811.05008/) (2018)
- [Learning-to-Rank with Partitioned Preference: Fast Estimation for the Plackett-Luce Model](https://mlsanity.com/paper/2006.05067/) (2020)
- [Learning Mixed Multinomial Logit Model from Ordinal Data](https://mlsanity.com/paper/1411.0073/) (2014)
- [Bayesian mixture of Plackett-Luce models for partially ranked data](https://mlsanity.com/paper/1501.03519/) (2015)
- [Modeling and Analysis of Tagging Networks in Stack Exchange Communities](https://mlsanity.com/paper/1902.02372/) (2019)
- [The Structure of U.S. College Networks on Facebook](https://mlsanity.com/paper/2006.04980/) (2020)
- [Scaling Choice Models of Relational Social Data](https://mlsanity.com/paper/2006.10003/) (2020)
- [Mixed Logit Models and Network Formation](https://mlsanity.com/paper/2006.16516/) (2020)
- [Emergence of Hierarchy in Networked Endorsement Dynamics](https://mlsanity.com/paper/2007.04448/) (2020)
- [Network interpolation](https://mlsanity.com/paper/1905.01253/) (2019)
- [The Dynamics of Faculty Hiring Networks](https://mlsanity.com/paper/2105.02949/) (2021)
- [Networks of climate change: Connecting causes and consequences](https://mlsanity.com/paper/2105.12537/) (2021)

## Built on by (most cited first, 1 of 1)

- [Generalized Top-k Mallows Model for Ranked Choices](https://mlsanity.com/paper/2510.22040/) (2025)

## Abstract (arXiv)

Multinomial Logit (MNL) is one of the most popular discrete choice models and has been widely used to model ranking data. However, there is a long-standing technical challenge of learning MNL from many real-world ranking data: exact calculation of the MNL likelihood of partial rankings is generally intractable. In this work, we develop a scalable method for approximating the MNL likelihood of general partial rankings in polynomial time complexity. We also extend the proposed method to learn mixture of MNL. We demonstrate that the proposed methods are particularly helpful for applications to choice-based network formation modeling, where the formation of new edges in a network is viewed as individuals making choices of their friends over a candidate set. The problem of learning mixture of MNL models from partial rankings naturally arises in such applications. And the proposed methods can be used to learn MNL models from network data without the strong assumption that temporal orders of all the edge formation are available. We conduct experiments on both synthetic and real-world network data to demonstrate that the proposed methods achieve more accurate parameter estimation and better fitness of data compared to conventional methods.