Hidden Markov Models with mixtures as emission distributions

In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the classical EM algorithm can be adapted to infer the model parameters. For the initialisation step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the merging criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN.

Unsupervised Classification for Tiling Arrays: ChIP-chip and Transcriptome

Tiling arrays make possible a large scale exploration of the genome thanks to probes which cover the whole genome with very high density until 2 000 000 probes. Biological questions usually addressed are either the expression difference between two conditions or the detection of transcribed regions. In this work we propose to consider simultaneously both questions as an unsupervised classification problem by modeling the joint distribution of the two conditions. In contrast to previous methods, we account for all available information on the probes as well as biological knowledge like annotation and spatial dependence between probes. Since probes are not biologically relevant units we propose a classification rule for non-connected regions covered by several probes. Applications to transcriptomic and ChIP-chip data of Arabidopsis thaliana obtained with a NimbleGen tiling array highlight the importance of a precise modeling and the region classification.