Inference algorithms for models based on Luce's choice axiom.
Project description
# choix
choix is a Python library that provides inference algorithms for models based on Luce’s choice axiom. These (probabilistic) models can be used to explain and predict outcomes of comparisons between items.
Pairwise comparisons: when the data consists of comparisons between two items, the model variant is usually referred to as the Bradley-Terry model. It is closely related to the Elo rating system used to rank chess players.
Partial rankings: when the data consists of rankings over (a subset of) the items, the model variant is usually referred to as the Plackett-Luce model.
Top-1 lists: another variation of the model arises when the data consists of discrete choices, i.e., we observe the selection of one item out of a subset of items.
choix makes it easy to infer model parameters from these different types of data, using a variety of algorithms:
Luce Spectral Ranking<sup>
Minorization-Maximization
Rank Centrality
Rank breaking
Approximate bayesian inference with expectation propagation
## Current state
Under active development, use at your own risk.
## References
Lucas Maystre and Matthias Grossglauser, Fast and Accurate Inference of Plackett-Luce Models, NIPS, 2015
David R. Hunter. MM algorithms for generalized Bradley-Terry models, The Annals of Statistics 32(1):384-406, 2004.
François Caron and Arnaud Doucet. Efficient Bayesian Inference for Generalized Bradley-Terry models. Journal of Computational and Graphical Statistics, 21(1):174-196, 2012.
Sahand Negahban, Sewoong Oh, and Devavrat Shah, Iterative Ranking from Pair-wise Comparison, NIPS 2012
Hossein Azari Soufiani, William Z. Chen, David C. Parkes, and Lirong Xia, Generalized Method-of-Moments for Rank Aggregation, NIPS 2013
Wei Chu and Zoubin Ghahramani, Extensions of Gaussian processes for ranking: semi-supervised and active learning, NIPS 2005 Workshop on Learning to Rank.
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