B0525
Title: Kernel ordinary differential equations
Authors: Xiaowu Dai - UCLA (United States) [presenting]
Abstract: The ordinary differential equation (ODE) is widely used in modelling biological and physical processes in science. A new reproducing kernel-based approach is proposed for the estimation and inference of ODE given noisy observations. The functional forms in ODE are assumed to be known or restricted to be linear or additive, and pairwise interactions are allowed. Sparse estimation is performed to select individual functionals and construct confidence intervals for the estimated signal trajectories. The estimation optimality and selection consistency of kernel ODE are established under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. The proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA too.
