Estimation of nonparametric dynamical models within Reproducing Kernel Hilbert Spaces for network inference

Florence d'Alché-Buc (1, 2) , Néhémy Lim (1) , George Michailidis (3) , Yasin Senbabaoglu (4)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 TAO - Machine Learning and Optimisation
3 Department of Statistics
4 DCM&B - Department of Computational Medicine and Bioinformatics

We consider the problem of network inference that occurs for instance in systems biology. A dynamical system (a gene regulatory network) is observed through time and the goal is to infer the dependence structure between state variables (mRNAs concentrations) from time series. Works concerning net- work inference usually rely on sparse linear models estimation or Granger causality tools. A very few address the issue in the nonlinear cases. In this work, we propose a nonparametric approach to dynamical system modeling that makes no assumption about the nature of the underlying nonlinear system. We develop a general framework based on Reproducing Kernel Hilbert Spaces based on matrix-valued kernels to identify the dynamical system and retrieve the target network. As in the linear case, the network inference task calls for sparsity control. We show very good results both in autoregressive models and differential equations estimation on DREAM benchmarks as well as on the IRMA datasets.

Keywords: ordinary differential equations; network inference; autoregressive models; nonparametric dynamical systems; systems biology; reproducing kernel Hilbert space; matrix-valued kernels

Domains: Statistics [stat]; Machine Learning [stat.ML]; Computer Science [cs]; Machine Learning [cs.LG]

Florence d'Alché-Buc, Néhémy Lim, George Michailidis, Yasin Senbabaoglu. Estimation of nonparametric dynamical models within Reproducing Kernel Hilbert Spaces for network inference. Parameter Estimation for Dynamical Systems - PEDS II, Bart Bakker, Shota Gugushvili, Chris Klaassen, Aad van der Vaart, Jun 2012, Eindhoven, Netherlands. ⟨hal-01084145⟩