# Latent Force Models with Gaussian Processes

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**Pattern Recognition Applications Group, Department of Electrical and Electronic Engineering, University of Cagliari, Italy**on Jul 13, 2009 [pdf]

#### Abstract

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 firstly give a brief introduction to Gaussian processes, then 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 motion capture.