# Latent Force Models: Combining the Mechanistic and Data Driven Modelling Paradigms

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**Rank Prize Workshop, Grasmere, Lake District**on Mar 28, 2012 [pdf]

#### Abstract

The main focus of machine learning is to combine data with assumptions that reflect our belief about the regularity of the world. This, then, allows us to generalize and make new predictions for ‘test data’. Relative to other modelling paradigms such as those found in physics that are based on mechanistic understandings of the world, models in machine learning typically make only weak assumptions about data.\ \ In this talk, we argue that these weak assumptions are also mechanistic in nature. In particular, a very common assumption is smoothness, which can arise through the heat equation or other models of diffusion. Our assumption of smoothness reflects our belief in an underlying physical world in which smoothness is the norm. Strong mechanistic models, such as those used in computational fluid dynamics, climate etc. typically impose much more rigid constraints on the data and are often inappropriate for machine learning tasks where the model needs to be adaptive and should still perform well even when our mechanistic assumptions are not completely fulfilled. These strong mechanistic frameworks can, however, incorporate regularities beyond smoothness. Systems with inertia exhibit resonance and oscillation and these can be easily incorporated with strong mechanistic assumptions.\ \ We believe that the area between the strong and weak mechanistic paradigms should be a focus for much more research. For many interesting datasets we need adaptive models which include mechanistic assumptions. The latent force modeling paradigm is one way of approaching this which relies on the combination of differential equation systems which are driven, or have their initial or boundary conditions set, by Gaussian processes. The Gaussian processes provide the necessary adaptability and the differential equation encodes mechanistic assumptions. In this talk we introduce the model and demonstrate results in motion capture date and, given time, computational biology.