Continuously indexed Potts models on unoriented graphs

Loic Landrieu, Guillaume Obozinski Ecole des Ponts ParisTech
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:588-597, 2014.

Abstract

This paper introduces an extension to undirected graphical models of the classical continuous time Markov chains. This model can be used to solve a transductive or unsupervised multi-class classification problem at each point of a network defined as a set of nodes connected by segments of different lengths. The classification is performed not only at the nodes, but at every point of the edge connecting two nodes. This is achieved by constructing a Potts process indexed by the continuum of points forming the edges of the graph. We propose a homogeneous parameterization which satisfies Kolmogorov consistency, and show that classical inference and learning algorithms can be applied. We then apply our model to a problem from geomatics, namely that of labelling city blocks automatically with a simple typology of classes (e.g. collective housing) from simple properties of the shape and sizes of buildings of the blocks. Our experiments shows that our model outperform standard MRFs and a discriminative model like logistic regression.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-landrieu14a, title = {Continuously indexed Potts models on unoriented graphs}, author = {Landrieu, Loic and ParisTech, Guillaume Obozinski Ecole des Ponts}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {588--597}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/landrieu14a/landrieu14a.pdf}, url = {https://proceedings.mlr.press/r12/landrieu14a.html}, abstract = {This paper introduces an extension to undirected graphical models of the classical continuous time Markov chains. This model can be used to solve a transductive or unsupervised multi-class classification problem at each point of a network defined as a set of nodes connected by segments of different lengths. The classification is performed not only at the nodes, but at every point of the edge connecting two nodes. This is achieved by constructing a Potts process indexed by the continuum of points forming the edges of the graph. We propose a homogeneous parameterization which satisfies Kolmogorov consistency, and show that classical inference and learning algorithms can be applied. We then apply our model to a problem from geomatics, namely that of labelling city blocks automatically with a simple typology of classes (e.g. collective housing) from simple properties of the shape and sizes of buildings of the blocks. Our experiments shows that our model outperform standard MRFs and a discriminative model like logistic regression.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Continuously indexed Potts models on unoriented graphs %A Loic Landrieu %A Guillaume Obozinski Ecole des Ponts ParisTech %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-landrieu14a %I PMLR %P 588--597 %U https://proceedings.mlr.press/r12/landrieu14a.html %V R12 %X This paper introduces an extension to undirected graphical models of the classical continuous time Markov chains. This model can be used to solve a transductive or unsupervised multi-class classification problem at each point of a network defined as a set of nodes connected by segments of different lengths. The classification is performed not only at the nodes, but at every point of the edge connecting two nodes. This is achieved by constructing a Potts process indexed by the continuum of points forming the edges of the graph. We propose a homogeneous parameterization which satisfies Kolmogorov consistency, and show that classical inference and learning algorithms can be applied. We then apply our model to a problem from geomatics, namely that of labelling city blocks automatically with a simple typology of classes (e.g. collective housing) from simple properties of the shape and sizes of buildings of the blocks. Our experiments shows that our model outperform standard MRFs and a discriminative model like logistic regression. %Z Reissued by PMLR on 04 October 2026.
APA
Landrieu, L. & ParisTech, G.O.E.d.P.. (2014). Continuously indexed Potts models on unoriented graphs. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:588-597 Available from https://proceedings.mlr.press/r12/landrieu14a.html. Reissued by PMLR on 04 October 2026.

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