We are used to dealing with the situation where we have a latent variable. Often we assume this latent variable to be independently drawn from a distribution, e.g. probabilistic PCA or factor analysis. This simplification is often extended for temporal data where tractable Markovian independence assumptions are used (e.g. Kalman filters or hidden Markov models).
In this talk we will consider the more general case where the latent variable is a forcing function in a differential equation model. We will show how for some simple ordinary differential equations the latent variable can be dealt with analytically for particular Gaussian process priors over the latent force. In this talk we will introduce the general framework, present results in systems biology and preview extensions.
Joint work with Magnus Rattray, Mauricio Álvarez, Pei Gao, Antti Honkela, David Luengo, Guido Sanguinetti and Michalis K. Titsias.