Recent years have witnessed a surge of interest for biological network discovery from experimental data due to the growing abundance of high-throughput « omics » data. Starting from two different problems in bioinformatics, protein-protein interaction prediction and gene regulatory network inference, we derive two approaches, one based on link prediction and the other, based on dynamical modeling of the behavior of the network to address network inference. Both cases raise the issue of regression in a structured output space or in a multiple output space. We present a set of new tools, we called Input Output Kernel Regression (IOKR) based on operator-valued kernels, that allows to build nonparametric models with values in a chosen output feature space, associated with an output kernel. When dealing with outputs in a Hilbert Space, operator-valued kernels are appropriate tools we use in the framework of Reproducing Kernel Hilbert Space Theory. We first develop new models derived from representer theorems in the case of supervised and semi-supervised learning in the context of this RKHS theory and also develop appropriate kernels and learning algorithms for both tasks (link prediction and dynamical modeling). The proposed methods provide very good performance on artificial and real datasets. Finally, we will draw some research perspectives first in computational biology and then more generally in structured regression.

Some related papers:

C. Brouard, F. d'Alch'e-Buc, M. Szafranski, Semi-supervised output kernel regression for link prediction, proceedings of the Twenty-Eighth Int. Conf. on Machine Learning (ICML 2011), Bellevue, Washington, June 28-July 2, pp. 593-600, 2011.

N. Lim, Y. Senbabaoglu, G. Michailidis, F. d'Alché-Buc. OKVAR-Boost: a novel boosting algorithm to infer nonlinear dynamics and gene regulatory interactions, Bioinformatics, April, 10, (advanced acces), 2013.

N. Lim, F. d’Alché-Buc, C. Auliac, G. Michailidis, Network inference and operator-valued kernel and vector autoregressive model, submitted to Machine Learning Journal.