On Parameter Priors for Discrete DAG Models

Dmitry Rusakov, Dan Geiger
Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, PMLR R3:259-264, 2001.

Abstract

We investigate parameter priors for discrete DAG models. It was shown in previous works that a Dirichlet prior on the parameters of a discrete DAG model is inevitable assuming global and local parameter independence for all possible complete DAG structures. A similar result for Gaussian DAG models hinted that the assumption of local independence may be redundant. Herein, we prove that the local independence assumption is necessary in order to dictate a Dirichlet prior on the parameters of a discrete DAG model. We explicate the minimal set of assumptions needed to dictate a Dirichlet prior, and we derive the functional form of prior distributions that arise under the global independence assumption alone.

Cite this Paper


BibTeX
@InProceedings{pmlr-vR3-rusakov01a, title = {On Parameter Priors for Discrete {DAG} Models}, author = {Rusakov, Dmitry and Geiger, Dan}, booktitle = {Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics}, pages = {259--264}, year = {2001}, editor = {Richardson, Thomas S. and Jaakkola, Tommi S.}, volume = {R3}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r3/rusakov01a/rusakov01a.pdf}, url = {http://proceedings.mlr.press/r3/rusakov01a.html}, abstract = {We investigate parameter priors for discrete DAG models. It was shown in previous works that a Dirichlet prior on the parameters of a discrete DAG model is inevitable assuming global and local parameter independence for all possible complete DAG structures. A similar result for Gaussian DAG models hinted that the assumption of local independence may be redundant. Herein, we prove that the local independence assumption is necessary in order to dictate a Dirichlet prior on the parameters of a discrete DAG model. We explicate the minimal set of assumptions needed to dictate a Dirichlet prior, and we derive the functional form of prior distributions that arise under the global independence assumption alone.}, note = {Reissued by PMLR on 31 March 2021.} }
Endnote
%0 Conference Paper %T On Parameter Priors for Discrete DAG Models %A Dmitry Rusakov %A Dan Geiger %B Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2001 %E Thomas S. Richardson %E Tommi S. Jaakkola %F pmlr-vR3-rusakov01a %I PMLR %P 259--264 %U http://proceedings.mlr.press/r3/rusakov01a.html %V R3 %X We investigate parameter priors for discrete DAG models. It was shown in previous works that a Dirichlet prior on the parameters of a discrete DAG model is inevitable assuming global and local parameter independence for all possible complete DAG structures. A similar result for Gaussian DAG models hinted that the assumption of local independence may be redundant. Herein, we prove that the local independence assumption is necessary in order to dictate a Dirichlet prior on the parameters of a discrete DAG model. We explicate the minimal set of assumptions needed to dictate a Dirichlet prior, and we derive the functional form of prior distributions that arise under the global independence assumption alone. %Z Reissued by PMLR on 31 March 2021.
APA
Rusakov, D. & Geiger, D.. (2001). On Parameter Priors for Discrete DAG Models. Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R3:259-264 Available from http://proceedings.mlr.press/r3/rusakov01a.html. Reissued by PMLR on 31 March 2021.

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