# Latent Variables, Differential Equations and Gaussian Processes

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**Microsoft Research, Cambridge, U.K.**on Nov 12, 2007 [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 such models in the context of a biological problem: inferring transcription factor activities in simple transcription networks. We will extend the simpler formalisms described above to consider the case where the latent variable is a â€™latent functionâ€™ and the relationship with the observed data is described by a linear differential equation. Through the use of a Gaussian process prior over the latent function we can perform inference tractably and learn parameters of interest in the system.