A New Probabilistic Approach in Rank Regression with Optimal Bayesian Partitioning
Abstract
In this paper, we consider the supervised learning task which consists in predicting the normalized rank of a numerical variable. We introduce a novel probabilistic approach to estimate the posterior distribution of the target rank conditionally to the predictors. We turn this learning task into a model selection problem. For that, we define a 2D partitioning family obtained by discretizing numerical variables and grouping categorical ones and we derive an analytical criterion to select the partition with the highest posterior probability. We show how these partitions can be used to build univariate predictors and multivariate ones under a naive Bayes assumption.
Cite
Text
Hue and Boullé. "A New Probabilistic Approach in Rank Regression with Optimal Bayesian Partitioning." Journal of Machine Learning Research, 2007.Markdown
[Hue and Boullé. "A New Probabilistic Approach in Rank Regression with Optimal Bayesian Partitioning." Journal of Machine Learning Research, 2007.](https://mlanthology.org/jmlr/2007/hue2007jmlr-new/)BibTeX
@article{hue2007jmlr-new,
title = {{A New Probabilistic Approach in Rank Regression with Optimal Bayesian Partitioning}},
author = {Hue, Carine and Boullé, Marc},
journal = {Journal of Machine Learning Research},
year = {2007},
pages = {2727-2754},
volume = {8},
url = {https://mlanthology.org/jmlr/2007/hue2007jmlr-new/}
}