  One of the focus areas of modern scientific research is to reveal mysteries
related to genes and their interactions. The dynamic interactions between genes
can be encoded into a gene regulatory network (GRN), which can be used to gain
understanding on the genetic mechanisms behind observable phenotypes. GRN
inference from time series data has recently been a focus area of systems
biology. Due to low sampling frequency of the data, this is a notoriously
difficult problem. We tackle the challenge by introducing the so-called
continuous-time Gaussian process dynamical model, based on Gaussian process
framework that has gained popularity in nonlinear regression problems arising
in machine learning. The model dynamics are governed by a stochastic
differential equation, where the dynamics function is modelled as a Gaussian
process. We prove the existence and uniqueness of solutions of the stochastic
differential equation. We derive the probability distribution for the Euler
discretised trajectories and establish the convergence of the discretisation.
We develop a GRN inference method called BINGO, based on the developed
framework. BINGO is based on MCMC sampling of trajectories of the GPDM and
estimating the hyperparameters of the covariance function of the Gaussian
process. Using benchmark data examples, we show that BINGO is superior in
dealing with poor time resolution and it is computationally feasible.
