%0 Journal Article %1 Smith2003b %A Smith, J. Q. %A Croft, J. %D 2003 %J Journal of Multivariate Analysis %K Graphical models %N 2 %P 387 - 402 %R DOI: 10.1016/S0047-259X(02)00067-2 %T Bayesian networks for discrete multivariate data: an algebraic approach to inference %U http://www.sciencedirect.com/science/article/B6WK9-4806GJ3-9/2/009b39fdce41806005c14e6072047f04 %V 84 %X In this paper we demonstrate how Gr�bner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gr�bner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.

@article{Smith2003b, abstract = {In this paper we demonstrate how Gr�bner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gr�bner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.}, added-at = {2009-09-12T19:19:34.000+0200}, author = {Smith, J. Q. and Croft, J.}, biburl = {https://www.bibsonomy.org/bibtex/26b67d0c38b4f161a3dafff5ae37507ea/mozaher}, doi = {DOI: 10.1016/S0047-259X(02)00067-2}, file = {:Smith2003b.pdf:PDF}, interhash = {1e3f16c303c09b0907671eae90211d45}, intrahash = {6b67d0c38b4f161a3dafff5ae37507ea}, issn = {0047-259X}, journal = {Journal of Multivariate Analysis}, keywords = {Graphical models}, number = 2, owner = {Mozaherul Hoque}, pages = {387 - 402}, timestamp = {2009-09-12T19:19:42.000+0200}, title = {Bayesian networks for discrete multivariate data: an algebraic approach to inference}, url = {http://www.sciencedirect.com/science/article/B6WK9-4806GJ3-9/2/009b39fdce41806005c14e6072047f04}, volume = 84, year = 2003 }