Learning a Mixture of Two Multinomial Logits
Abstract
The classical Multinomial Logit (MNL) is a behavioral model for user choice. In this model, a user is offered a slate of choices (a subset of a finite universe of $n$ items), and selects exactly one item from the slate, each with probability proportional to its (positive) weight. Given a set of observed slates and choices, the likelihood-maximizing item weights are easy to learn at scale, and easy to interpret. However, the model fails to represent common real-world behavior. As a result, researchers in user choice often turn to mixtures of MNLs, which are known to approximate a large class of models of rational user behavior. Unfortunately, the only known algorithms for this problem have been heuristic in nature. In this paper we give the first polynomial-time algorithms for exact learning of uniform mixtures of two MNLs. Interestingly, the parameters of the model can be learned for any $n$ by sampling the behavior of random users only on slates of sizes 2 and 3; in contrast, we show that slates of size 2 are insufficient by themselves.
Cite
Text
Chierichetti et al. "Learning a Mixture of Two Multinomial Logits." International Conference on Machine Learning, 2018.Markdown
[Chierichetti et al. "Learning a Mixture of Two Multinomial Logits." International Conference on Machine Learning, 2018.](https://mlanthology.org/icml/2018/chierichetti2018icml-learning/)BibTeX
@inproceedings{chierichetti2018icml-learning,
title = {{Learning a Mixture of Two Multinomial Logits}},
author = {Chierichetti, Flavio and Kumar, Ravi and Tomkins, Andrew},
booktitle = {International Conference on Machine Learning},
year = {2018},
pages = {961-969},
volume = {80},
url = {https://mlanthology.org/icml/2018/chierichetti2018icml-learning/}
}