Variational Inference under the Plackett-Luce Model

The present code computes the parameter vector and metric result under the Plackett Luce model.

The code in this repository provides a framework for variational inference computation ranking data. In particular, the algorithms implemented are described in the paper:

"Variational Inference from Ranked Samples with Features", Yuan Guo, Jennifer Dy, Deniz Erdogmus, Jayashree Kalpathy-Cramer, Susan Ostmo, J.Peter Campbell, Michael F.Chiang and Stratis Ioannidis. In Asian Conference on
Machine Learning, pp. 599-614. 2019.

Please cite this paper if you intend to use this code for your research.

functionpackage.py

The python file includes the following modules:

numpy
scipy
random

Function EMPlackett:

The EM function to compute the variational inference mean and covariance matrix.

This file will return the mean, covariance matrix and lower bound. The input variables are:

(Xarray,RankPlack,C_value,args.loopT) 

• Xarray is the feature matrix for N absolute samples.

• RankPlack is the dictionary for the ranking index.

• C_value is a variable for prior Gaussian distribution .

• args.loopT is the iteration number for inner altermation.

Function MapEstimation:

The Newton method to compute the parameter estimation of MAP.

This file will return the parameter vector. The input variables are:

(Xarray,RankMul,C_value) 

• Xarray is the feature matrix for N absolute samples.

• RankMul is the dictionary for the ranking index （with top query form).

• C_value is a variable for prior Gaussian distribution .

Acknowledgement

Our work is supported by NIH (R01EY019474, P30EY10572), NSF (SCH-1622542 at MGH; SCH-1622536 at Northeastern; SCH-1622679 at OHSU), and by unrestricted departmental funding from Research to Prevent Blindness (OHSU).