Parametric Modelling of Multivariate Count Data Using Probabilistic Graphical Models

Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and ecology (where the data can represent, for example, children counts associated with multitype branching processes), sociology and econometrics. We focus on I) Identifying categories that appear simultaneously, or on the contrary that are mutually exclusive. This is achieved by identifying conditional independence relationships between the variables; II)Building parsimonious parametric models consistent with these relationships; III) Characterising and testing the effects of covariates on the joint distribution of the counts. To achieve these goals, we propose an approach based on graphical probabilistic models, and more specifically partially directed acyclic graphs

Quantification de l'incertitude sur la structure latente dans des modèles de Markov cachés

National audienceNous introduisons les modèles de Markov cachés graphiques, qui généralisent les chaînes et arbres de Markov cachés (CMCs et AMCs). Nous montrons comment l'incertitude globale sur le processus d'état caché peut être décomposée en une somme d'entropies conditionnelles, qui s'interprètent comme une contribution locale à l'incertitude globale. Nous donnons un algorithme efficace de calcul de ces entropies pour les CMCs et AMCs et montrons leur apport, en complément d'autres algorithmes de restauration des états, au diagnostic et à l'interprétation des états cachés. Nous montrons également que les profils classiques de probabilités lissées (loi marginale de l'état caché à chaque instant, sachant l'ensemble des observations), ne permet pas de conclure sur la contribution locale à l'incertitude globale

Approche graphique pour la modélisation statistique de la dépendance entre activités journalières

http://mistis.inrialpes.fr/workshop-statistique-transport.html Transparents disponibles sur http://mistis.inrialpes.fr/docs/workshop-statistique-transport/slidesDurand.pdfInternational audienceIn this presentation, we introduce a new family of statistical models for the analysis of multivariate count data. We propose an application in modelling daily activity programs at the scale of individuals or families

Estimation of Discrete Partially Directed Acyclic Graphical Models in Multitype Branching Processes

International audienceWe address the inference of discrete-state models for tree-structured data. Our aim is to introduce parametric multitype branching processes that can be efficiently estimated on the basis of data of limited size. Each generation distribution within this macroscopic model is modeled by a partially directed acyclic graphical model. The estimation of each graphical model relies on a greedy algorithm for graph selection. We present an algorithm for discrete graphical model which is applied on multivariate count data. The proposed modeling approach is illustrated on plant architecture datasets

Computational methods for hidden Markov tree models - An application to wavelet trees.

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1323262International audienceThe hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and called it the 'upward-downward algorithm'. This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new 'upward-downward' algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes

Détection de motifs disruptifs au sein de plantes : une approche de quotientement/classification d'arborescences

National audienceMultiple change-point models for path-indexed data are transposed to tree-indexed data. The objective of multiple change-point models is to partition a heterogeneous tree into homogeneous subtrees. Since optimal algorithms for segmenting sequences cannot be transposed to trees, we propose here an efficient heuristic for tree segmentation. Segmented subtrees are grouped together in a post-processing phase since similar disjoint patches are often observed in tree canopy. Application of such models is illustrated on mango tree where subtrees are assimilated to plant patches and clusters of patches to patch types (e.g. vegetative, flowering or resting patch).Les modèles de détection de ruptures multiples pour séquences sont transposés aux arborescences. L'objectif est de quotienter une arborescence en sous-arborescences homogènes. Comme les algorithmes optimaux de segmentation de séquences ne peuvent être transposés aux arborescences, nous proposons ici une méthode heuristique permettant de segmenter efficacement une arborescence. Les sous-arborescences obtenues sont ensuite groupées dans une phase de post-traitement car des sous-arborescences disjointes relativement similaires sont observées dans les canopées d'arbre. Ces modèles sont illustrés par le cas du manguier où les collections de sous-arborescences permettent d'identifier les motifs disruptifs (juxtaposition de sous-arborescences végétatives, florifères ou en pause) observés dans les canopées

Compétitions d’analyse des données à l’Université Grenoble Alpes : motivations, organisation et retours d’expérience

National audienc