scholarly journals Linear Extensions and Comparable Pairs in Partial Orders

Order ◽  
2017 ◽  
Vol 35 (3) ◽  
pp. 403-420 ◽  
Author(s):  
Colin McDiarmid ◽  
David Penman ◽  
Vasileios Iliopoulos
Keyword(s):  
Partial Orders ◽  
Linear Extensions

scholarly journals Learning Plackett-Luce Mixtures from Partial Preferences

2019 ◽  
Vol 33 ◽  
pp. 4328-4335
Author(s):  
Ao Liu ◽  
Zhibing Zhao ◽  
Chao Liao ◽  
Pinyan Lu ◽  
Lirong Xia
Keyword(s):  
Gibbs Sampler ◽  
Synthetic Data ◽  
Partial Orders ◽  
Linear Extensions ◽  
Real World Data ◽  
Test Dataset ◽  
The Core ◽  
Insertion Method ◽  
Efficient Sampling ◽  
Luce Model

We propose an EM-based framework for learning Plackett-Luce model and its mixtures from partial orders. The core of our framework is the efficient sampling of linear extensions of partial orders under Plackett-Luce model. We propose two Markov Chain Monte Carlo (MCMC) samplers: Gibbs sampler and the generalized repeated insertion method tuned by MCMC (GRIM-MCMC), and prove the efficiency of GRIM-MCMC for a large class of preferences.Experiments on synthetic data show that the algorithm with Gibbs sampler outperforms that with GRIM-MCMC. Experiments on real-world data show that the likelihood of test dataset increases when (i) partial orders provide more information; or (ii) the number of components in mixtures of PlackettLuce model increases.

scholarly journals Linear extensions of partial orders and reverse mathematics

2012 ◽  
Vol 58 (6) ◽  
pp. 417-423 ◽  
Author(s):  
Emanuele Frittaion ◽  
Alberto Marcone
Keyword(s):  
Reverse Mathematics ◽  
Partial Orders ◽  
Linear Extensions

scholarly journals On Unimodality for Linear Extensions of Partial Orders

1980 ◽  
Vol 1 (4) ◽  
pp. 405-410 ◽  
Author(s):  
F. R. K. Chung ◽  
P. C. Fishburn ◽  
R. L. Graham
Keyword(s):  
Partial Orders ◽  
Linear Extensions

Evaluation of the ranking probabilities for partial orders based on random linear extensions

Chemosphere ◽  
2003 ◽  
Vol 53 (8) ◽  
pp. 981-992 ◽  
Author(s):  
Dorte Lerche ◽  
Peter B. Sørensen
Keyword(s):  
Partial Orders ◽  
Linear Extensions
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