Bézier Curve Gaussian Processes

Probabilistic models for sequential data are the basis for a variety of applications concerned with processing timely ordered information. The predominant approach in this domain is given by neural networks, which incorporate either stochastic units or components. This paper proposes a new probabilistic sequence model building on probabilistic B\'ezier curves. Using Gaussian distributed control points, these parametric curves pose a special case for Gaussian processes (GP). Combined with a Mixture Density network, Bayesian conditional inference can be performed without the need for mean field variational approximation or Monte Carlo simulation, which is a requirement of common approaches. For assessing this hybrid model's viability, it is applied to an exemplary sequence prediction task. In this case the model is used for pedestrian trajectory prediction, where a generated prediction also serves as a GP prior. Following this, the initial prediction can be refined using the GP framework by calculating different posterior distributions, in order to adapt more towards a given observed trajectory segment.