"Breaking non-identifiability using genetic information : an application to metabolite data and gene expression"

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• Benjamin Frot, University of Oxford
• Tuesday 08 November 2016, 14:30-15:30
• Large Seminar Room, 1st Floor, Institute of Public Health, University Forvie Site, Robinson Way, Cambridge.

If you have a question about this talk, please contact Alison Quenault.

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random field into the sum of a sparse and a low-rank matrix. We derive convergence bounds for this estimator and show that it is well-behaved in the high-dimensional regime as well as “sparsistent” (i.e. capable of recovering the graph structure). We then show how proximal gradient algorithms and semi-definite programming techniques can be employed to fit the model to thousands of variables. Through extensive simulations, we illustrate the conditions required for identifiability and show that there is a wide range of situations in which this model performs significantly better than its counterparts, e.g. it can accommodate more latent variables. Finally, the suggested method is applied to two datasets comprising genetic variants and metabolites levels. We show our results are well replicated across datasets and assess their biological relevance using an external source of validation. We also apply it to a human gene expression dataset.

This talk is part of the MRC Biostatistics Unit Seminars series.

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