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

Abstract : 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.