Efficient Stepwise Selection in Decomposable Models
Abstract
In this paper, we present an efficient algorithm for performing stepwise selection in the class of decomposable models. We focus on the forward selection procedure, but we also discuss how backward selection and the combination of the two can be performed efficiently. The main contributions of this paper are (1) a simple characterization for the edges that can be added to a decomposable model while retaining its decomposability and (2) an efficient algorithm for enumerating all such edges for a given decomposable model in O(n2) time, where n is the number of variables in the model. We also analyze the complexity of the overall stepwise selection procedure (which includes the complexity of enumerating eligible edges as well as the complexity of deciding how to "progress"). We use the KL divergence of the model from the saturated model as our metric, but the results we present here extend to many other metrics as well.
Cite
Text
Deshpande et al. "Efficient Stepwise Selection in Decomposable Models." Conference on Uncertainty in Artificial Intelligence, 2001.Markdown
[Deshpande et al. "Efficient Stepwise Selection in Decomposable Models." Conference on Uncertainty in Artificial Intelligence, 2001.](https://mlanthology.org/uai/2001/deshpande2001uai-efficient/)BibTeX
@inproceedings{deshpande2001uai-efficient,
title = {{Efficient Stepwise Selection in Decomposable Models}},
author = {Deshpande, Amol and Garofalakis, Minos N. and Jordan, Michael I.},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2001},
pages = {128-135},
url = {https://mlanthology.org/uai/2001/deshpande2001uai-efficient/}
}