Gaussian Process Kernels for Popular State-Space Time Series Models

Peer reviewe

State space Gaussian processes with non-Gaussian likelihood

We provide a comprehensive overview and tooling for GP modelling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensonal GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF) / expectation propagation (EP) schemes has been largely overlooked. We present means of combining the efficient O(n) state space methodology with existing inference methods. We also furher extend existing methods, and provide unifying code implementing all approaches.Peer reviewe

Modeling an unsteady elastic diffusion processes in a Timoshenko plate.

We investigated unsteady elastic diffusion vibrations of a rectangular isotropic Timoshenko plate. For the mathematical problem formulation, a model of coupled elastic diffusion processes in a multicomponent continuum is used. Using the d'Alembert variational principle, the equations of transverse vibrations of a rectangular isotropic Timoshenko plate taking into account diffusion are obtained from this model. An initialboundary value problem of a simply supported plate bending is formulated