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.
- Choices in a network: when the data consists of counts of the number of visits to each node in a network, the model is known as the Network Choice Model.
choix makes it easy to infer model parameters from these different types of
data, using a variety of algorithms:
- Luce Spectral Ranking
- Minorization-Maximization
- Rank Centrality
- Approximate Bayesian inference with expectation propagation
To install the latest release directly from PyPI, simply type:
pip install choix
To get started, you might want to explore one of these notebooks:
- Introduction using pairwise-comparison data
- Case study: analyzing the GIFGIF dataset
- Using ChoiceRank to understand traffic on a network
- Approximate Bayesian inference using EP
You can also find more information on the official documentation. In particular, the API reference contains a good summary of the library's features.
- Hossein Azari Soufiani, William Z. Chen, David C. Parkes, and Lirong Xia, Generalized Method-of-Moments for Rank Aggregation, NIPS 2013
- François Caron and Arnaud Doucet. Efficient Bayesian Inference for Generalized Bradley-Terry models. Journal of Computational and Graphical Statistics, 21(1):174-196, 2012.
- Wei Chu and Zoubin Ghahramani, Extensions of Gaussian processes for ranking: semi-supervised and active learning, NIPS 2005 Workshop on Learning to Rank.
- David R. Hunter. MM algorithms for generalized Bradley-Terry models, The Annals of Statistics 32(1):384-406, 2004.
- Ravi Kumar, Andrew Tomkins, Sergei Vassilvitskii and Erik Vee, Inverting a Steady-State, WSDM 2015.
- Lucas Maystre and Matthias Grossglauser, Fast and Accurate Inference of Plackett-Luce Models, NIPS, 2015.
- Lucas Maystre and M. Grossglauser, ChoiceRank: Identifying Preferences from Node Traffic in Networks, ICML 2017.
- Sahand Negahban, Sewoong Oh, and Devavrat Shah, Iterative Ranking from Pair-wise Comparison, NIPS 2012.