Conditional products: An alternative approach to conditional independence

A. Philip Dawid, Milan Studený
Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, PMLR R2:27-35, 1999.

Abstract

We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factorization properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the "conditional product", which provides a way of combining the basic objects under consideration while preserving as much independence as possible. We introduce an appropriate axiom system for conditional product, and show how, when these axioms are obeyed, they induce a derived concept of conditional independence which obeys the usual semi-graphoid axioms. The general structure is used to throw light on three specific areas: the familiar probabilistic framework (both the discrete and the general case); a set-theoretic framework related to "variation independence"; and a variety of graphical frameworks.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR2-dawid99a, title = {Conditional products: An alternative approach to conditional independence}, author = {Dawid, A. Philip and Studen{\'{y}}, Milan}, booktitle = {Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics}, pages = {27--35}, year = {1999}, editor = {Heckerman, David and Whittaker, Joe}, volume = {R2}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r2/dawid99a/dawid99a.pdf}, url = {https://proceedings.mlr.press/r2/dawid99a.html}, abstract = {We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factorization properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the "conditional product", which provides a way of combining the basic objects under consideration while preserving as much independence as possible. We introduce an appropriate axiom system for conditional product, and show how, when these axioms are obeyed, they induce a derived concept of conditional independence which obeys the usual semi-graphoid axioms. The general structure is used to throw light on three specific areas: the familiar probabilistic framework (both the discrete and the general case); a set-theoretic framework related to "variation independence"; and a variety of graphical frameworks.}, note = {Reissued by PMLR on 20 August 2020.} }
Endnote
%0 Conference Paper %T Conditional products: An alternative approach to conditional independence %A A. Philip Dawid %A Milan Studený %B Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1999 %E David Heckerman %E Joe Whittaker %F pmlr-vR2-dawid99a %I PMLR %P 27--35 %U https://proceedings.mlr.press/r2/dawid99a.html %V R2 %X We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factorization properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the "conditional product", which provides a way of combining the basic objects under consideration while preserving as much independence as possible. We introduce an appropriate axiom system for conditional product, and show how, when these axioms are obeyed, they induce a derived concept of conditional independence which obeys the usual semi-graphoid axioms. The general structure is used to throw light on three specific areas: the familiar probabilistic framework (both the discrete and the general case); a set-theoretic framework related to "variation independence"; and a variety of graphical frameworks. %Z Reissued by PMLR on 20 August 2020.
APA
Dawid, A.P. & Studený, M.. (1999). Conditional products: An alternative approach to conditional independence. Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R2:27-35 Available from https://proceedings.mlr.press/r2/dawid99a.html. Reissued by PMLR on 20 August 2020.

Related Material