Semi-parametric Markov Tree for cell lineage analysis

Pierre Fernique (1, 2) , Jonathan Legrand (3) , Jean-Baptiste Durand (2, 4) , Yann Guédon (1, 2)

1 UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
3 RDP - Reproduction et développement des plantes
4 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

An enlarged family of hidden Markov out-tree models is introduced. Unlike state-of-the-art hidden Markov out-tree models, in these models child vertices are not independent given their parent vertex, and the number of children per parent is random. The upward-downward smoothing algorithm, which in particular is used to implement efficiently the E-step in the EM algorithm, and the dynamic programming algorithm which is used to restore of the most probable state tree, are derived for this family of models. The advantage of such models is illustrated on cell lineages in floral meristems where non-parametric generation distributions are coupled with parametric observation models in order to define semi-parametric hidden Markov out-tree models.

Mots clés: smoothing algorithm; hidden Markov out-tree model; cell lineage; dynamic programming algorithm; upward-downward algorithm; viterbi-algorithm

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]

Pierre Fernique, Jonathan Legrand, Jean-Baptiste Durand, Yann Guédon. Semi-parametric Markov Tree for cell lineage analysis. 2016. ⟨hal-01286298⟩