BayesMallows

This package provides a general framework for analyzing rank and preference data based on the Bayesian Mallows model first described in Vitelli et al.(2018).

Installation

To install the current release, use

install.packages("BayesMallows")

To install the current development version, use

#install.packages("remotes")
remotes::install_github("ocbe-uio/BayesMallows")

# Set build_vignettes to TRUE to also get the package vignette
remotes::install_github("ocbe-uio/BayesMallows", build_vignettes = TRUE)

Basic Usage Example

To get started, load the package with

library(BayesMallows)

The package comes with several example datasets. The simplest one contains 12 persons’ assessments of the weights of 20 potatoes, either by visual inspection (potato_visual) or by lifting the potatoes and comparing their relative weights by hand (potato_weighing). To fit a Bayesian Mallows model on the potato_visual dataset, we do

fit <- compute_mallows(potato_visual)

Next, we can see a diagnostic plot for the Metropolis-Hastings algorithm with assess_convergence(). The plot below is for the scale parameter, which measures the variation between the individual rankings.

assess_convergence(fit)

Setting the burnin to 500, we obtain a plot of the posterior distribution of the scale parameter with:

plot(fit, burnin = 500)

For more examples, please see the vignette, which is based on Sørensen et al. (2020), and the function documentation. The vignette can be opened by issuing the following command.

vignette("BayesMallows")

The Bayesian Mallows Model

Methodology

The BayesMallows package currently implements the complete model described in Vitelli et al. (2018), which includes a large number of distance metrics, handling of missing ranks and pairwise comparisons, and clustering of users with similar preferences. The extension to non-transitive pairwise comparisons by Crispino et al. (2019) is also implemented. In addition, the partition function of the Mallows model can be estimated using the importance sampling algorithm of Vitelli et al. (2018) and the asymptotic approximation of Mukherjee (2016). For a review of ranking models in general, see Q. Liu et al. (2019b). Crispino and Antoniano-Villalobos (2019) outlines how informative priors can be used within the model.

Applications

Among the current applications, Q. Liu et al. (2019a) applied the Bayesian Mallows model for providing personalized recommendations based on clicking data, and Barrett and Crispino (2018) used the model of Crispino et al. (2019) to analyze listeners’ understanding of music.

Future Extensions

Plans for future extensions of the package include allowing for analysis of time-varying ranks as described in Asfaw et al. (2016), (frequentist) maximum likelihood estimation, and implementation of a variational Bayes algorithm for approximation the posterior distribution.

Citation

If using the BayesMallows package in academic work, please cite Sørensen et al. (2020), in addition to the relevant methodological papers.

citation("BayesMallows")
#> 
#> Sørensen Ø, Crispino M, Liu Q, Vitelli V (2020). "BayesMallows: An R
#> Package for the Bayesian Mallows Model." _The R Journal_, *12*(1),
#> 324-342. doi: 10.32614/RJ-2020-026 (URL:
#> https://doi.org/10.32614/RJ-2020-026), <URL:
#> https://doi.org/10.32614/RJ-2020-026>.
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Article{,
#>     author = {{\O}ystein S{\o}rensen and Marta Crispino and Qinghua Liu and Valeria Vitelli},
#>     doi = {10.32614/RJ-2020-026},
#>     title = {BayesMallows: An R Package for the Bayesian Mallows Model},
#>     journal = {The R Journal},
#>     number = {1},
#>     pages = {324--342},
#>     volume = {12},
#>     url = {https://doi.org/10.32614/RJ-2020-026},
#>     year = {2020},
#>   }

Contribution

This is an open source project, and all contributions are welcome. Feel free to open an Issue, a Pull Request, or to e-mail us.

References

Asfaw, D., V. Vitelli, Ø Sørensen, E. Arjas, and A. Frigessi. 2016. “Time-Varying Rankings with the Bayesian Mallows Model.” Stat 6 (1): 14–30. https://doi.org/10.1002/sta4.132.

Barrett, N., and M. Crispino. 2018. “The Impact of 3-d Sound Spatialisation on Listeners’ Understanding of Human Agency in Acousmatic Music.” Journal of New Music Research 47 (5): 399–415. https://doi.org/10.1080/09298215.2018.1437187.

Crispino, M., and I. Antoniano-Villalobos. 2019. “Informative Extended Mallows Priors in the Bayesian Mallows Model.” https://arxiv.org/abs/1901.10870.

Crispino, M., E. Arjas, V. Vitelli, N. Barrett, and A. Frigessi. 2019. “A Bayesian Mallows Approach to Nontransitive Pair Comparison Data: How Human Are Sounds?” The Annals of Applied Statistics 13 (1): 492–519. https://doi.org/10.1214/18-aoas1203.

Liu, Q., A. H. Reiner, A. Frigessi, and I. Scheel. 2019a. “Diverse Personalized Recommendations with Uncertainty from Implicit Preference Data with the Bayesian Mallows Model.” Knowledge-Based Systems 186 (December): 104960. https://doi.org/10.1016/j.knosys.2019.104960.

Liu, Q, M Crispino, I Scheel, V Vitelli, and A Frigessi. 2019b. “Model-Based Learning from Preference Data.” Annual Review of Statistics and Its Application 6 (1). https://doi.org/10.1146/annurev-statistics-031017-100213.

Mukherjee, S. 2016. “Estimation in Exponential Families on Permutations.” The Annals of Statistics 44 (2): 853–75. https://doi.org/10.1214/15-aos1389.

Sørensen, Øystein, Marta Crispino, Qinghua Liu, and Valeria Vitelli. 2020. “BayesMallows: An R Package for the Bayesian Mallows Model.” The R Journal 12 (1): 324–42. https://doi.org/10.32614/RJ-2020-026.

Vitelli, V., Ø. Sørensen, M. Crispino, E. Arjas, and A. Frigessi. 2018. “Probabilistic Preference Learning with the Mallows Rank Model.” Journal of Machine Learning Research 18 (1): 1–49. https://jmlr.org/papers/v18/15-481.html.