ThesisPDF Available

A statistical modeling framework for analyzing tree-indexed data

  • December 2014
  • Thesis for: PhD
  • Advisor: Yann Guedon, Jean-Baptiste Durand
Authors:
Pierre Benjamin Fernique at Limagrain
Pierre Benjamin Fernique
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Abstract and Figures

We address statistical models for tree-indexed data.In Virtual Plants team, the host team for this thesis, applications of interest focus on plant development and its modulation by environmental and genetic factors.We thus focus on plant developmental applications both at a microscopic level with the study of the cell lineage in the biological tissue responsible for the plant growth, and at a macroscopic level with the mechanism of branch production.Far fewer models are available for tree-indexed data than for path-indexed data.This thesis therefore aims to propose a statistical modeling framework for studying patterns in tree-indexed data.To this end, two different classes of statistical models, Markov and change-point models, are investigated
The m-separation property. In the graph G 10 , 0 ⊥ 3|1, 2, 1 ⊥ 3|0, 4 (see G m 10 ) and 1 ⊥ 2 (see G 10 m an({0,1}) ) hold but not 1 ⊥ 2|3, 4 as the edge (1, 2) is added in the moral graph G m 10
The m-separation property. In the graph G 10 , 0 ⊥ 3|1, 2, 1 ⊥ 3|0, 4 (see G m 10 ) and 1 ⊥ 2 (see G 10 m an({0,1}) ) hold but not 1 ⊥ 2|3, 4 as the edge (1, 2) is added in the moral graph G m 10
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Remarkable mixed graphs. Graph G 8 is a mixed cyclic graph as there is the directed 4-cycle 0, 3, 2, 1, 0. On graph G 9 which is a MAG there is one u-shape implying the immorality (2, 3). Graph G m 9 , the moral graph of G 9 , is not chordal as the immorality (2, 3) in G 9 induced the addition of edge (2, 3) in comparison to its undirected version.
Remarkable mixed graphs. Graph G 8 is a mixed cyclic graph as there is the directed 4-cycle 0, 3, 2, 1, 0. On graph G 9 which is a MAG there is one u-shape implying the immorality (2, 3). Graph G m 9 , the moral graph of G 9 , is not chordal as the immorality (2, 3) in G 9 induced the addition of edge (2, 3) in comparison to its undirected version.
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The d-separation property. In graph G 7 as the vertices 0 and 1 are separated in G 7 m an({0,1}) , 1 ⊥ 0 does hold but not 1 ⊥ 0 | 2 as the immorality (0, 1) in G 7 m an({0,1,2}) is moralized thus vertices 0 and 1 are not separated by vertex 2.
The d-separation property. In graph G 7 as the vertices 0 and 1 are separated in G 7 m an({0,1}) , 1 ⊥ 0 does hold but not 1 ⊥ 0 | 2 as the immorality (0, 1) in G 7 m an({0,1,2}) is moralized thus vertices 0 and 1 are not separated by vertex 2.
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Examples of magnetic fields. (A) The south parallel field. (B) The polar one. (C) The clockwise concentric one. The ideal direction of directed edges are represented at given positions considering 3 of the magnetic fields proposed by Sugiyama and Misue (1995).
Examples of magnetic fields. (A) The south parallel field. (B) The polar one. (C) The clockwise concentric one. The ideal direction of directed edges are represented at given positions considering 3 of the magnetic fields proposed by Sugiyama and Misue (1995).
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Mersitem and example of tree-indexed data at microscopic scale (Fernandez, 2010; Legrand, 2014). (A) SAM of Arabidopsis thaliana photography and associated floral meristems. At some point, cells not maintained as embryonic cells in the SAM enter into the differentiation process of floral meristems. (B, C) Schematic cross-sections of a same meristem at different times are represented with identified cells (c t ) t∈0,11. The possible location of this cross-section is located on (A) with a dotted black line. Only the first two layers of cells L1 and L2 are represented in this scheme. (C) Tree representation of the follow up from (A) to (B) where each cell is represented by the corresponding labeled vertex and lineages are represented by directed edges. Cells of the first observation (A) are considered as roots of the trees and at each time, a cell is connected to itself at the precedent time if no division occurred and to its mother otherwise. Only two divisions occurred here, from cell 1 to cells 6 and 7 and from cell 2 to cells 8 and 9.
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Mersitem and example of tree-indexed data at microscopic scale (Fernandez, 2010; Legrand, 2014). (A) SAM of Arabidopsis thaliana photography and associated floral meristems. At some point, cells not maintained as embryonic cells in the SAM enter into the differentiation process of floral meristems. (B, C) Schematic cross-sections of a same meristem at different times are represented with identified cells (c t ) t∈0,11. The possible location of this cross-section is located on (A) with a dotted black line. Only the first two layers of cells L1 and L2 are represented in this scheme. (C) Tree representation of the follow up from (A) to (B) where each cell is represented by the corresponding labeled vertex and lineages are represented by directed edges. Cells of the first observation (A) are considered as roots of the trees and at each time, a cell is connected to itself at the precedent time if no division occurred and to its mother otherwise. Only two divisions occurred here, from cell 1 to cells 6 and 7 and from cell 2 to cells 8 and 9.
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Age States of Plants of Various Growth Forms: A Review AGE STATES OF PLANTS OF VARIOUS GROWTH FORMS: A REVIEW
Article
Full-text available
  • Jul 1980
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. British Ecological Society is collaborating with JSTOR to digitize, preserve and extend access to Journal of Ecology. SUMMARY (1) Analysis of more than one-hundred plant species has shown certain consistently recognizable biological age states in their ontogeny. These are called seed, seedling, juvenile, immature, virginile, reproductive (young, mature and old), subsenile and senile. (2) Each age state may be characterized by a particular combination of quantitative and qualitative features. Qualitative features used to define the various age states are: the manner of nutrition, the type of growth, the pattern of branching of the root and shoot systems, leaf form, the presence of a particular type of shoot, the ability to reproduce by seeds, the balance between living and dead structures, and the balance between actively-growing and fully-formed structures. (3) Quantitative characteristics change uninterruptedly during ontogeny, and as a rule follow a unimodal curve. (4) Age states of species representative of a variety of growth forms have been distinguished and described. These include trees, shrubs, semi-shrubs, low semi-shrubs, firm-and loose-tussock plants, and the following categories of perennial herbs: long-and short-rhizomed, root-suckering, stoloniferous, bulbous, tuber-bulbous, tuberous and tap-rooted. (5) On the basis of these age-state studies, three main types of ontogeny in polycarpic plants are defined, using as characterizing features architectural changes of the individual plant, the form and timing of break-up of the individual plant, and the extent of rejuvenation.
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Learning Bayesian Networks
Chapter
  • Dec 2007
This chapter addresses the problem of learning the parameters from data. It also discusses score-based structure learning and constraint-based structure learning. The method for learning all parameters in a Bayesian network follows readily from the method for learning a single parameter. The chapter presents a method for learning the probability of a binomial variable and extends this method to multinomial variables. It also provides guidelines for articulating the prior beliefs concerning probabilities. The chapter illustrates the constraint-based approach by showing how to learn a directed acyclic graph (DAG) faithful to a probability distribution. Structure learning consists of learning the DAG in a Bayesian network from data. It is necessary to know which DAG satisfies the Markov condition with the probability distribution P that is generating the data. The process of learning such a DAG is called “model selection.” A DAG includes a probability distribution P if the DAG does not entail any conditional independencies that are not in P. In score-based structure learning, a score is assigned to each DAG based on the data such that in the limit. After scoring the DAGs, the score are used, possibly along with prior probabilities, to learn a DAG. The most straightforward score, the Bayesian score, is the probability of the data D given the DAG. Once a DAG is learnt from data, the parameters can be known. The result will be a Bayesian network that can be used to do inference. In the constraint-based approach, a DAG is found for which the Markov condition entails all and only those conditional independencies that are in the probability distribution P of the variables of interest. The chapter applies structure learning to inferring causal influences from data and presents learning packages. It presents examples of learning Bayesian networks and of causal learning.
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