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 \emph{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.

本研究提出了一种用于近似计算一般偏序排名的 Multinomial Logit 概率的可扩展方法，特别在选择基于网络形成建模问题中的参数估计方面表现出更准确和更好的数据拟合。

利用一般部分排序快速学习MNL模型并应用于网络形成建模