Variational Inference and Learning for Continuous-Time Nonlinear State-Space Models
Antti Honkela, Markus Harva, Tapani Raiko, Juha Karhunen · 2008
Inference in continuous-time stochastic dynamical models is a challenging problem. To complement existing sampling-based methods [2], variational methods have recently been developed for this problem [1]. Our approach, which was first introduced in [3], solves the variational continuous-time inference problem by discretisation that essentially reduces it to a discrete-time problem previously considered in [8]. While this approach is not as elegant as that of [1], our framework makes learning the model in addition to inference easy. Other extensions such as heteroscedastic models are also relatively easy to consider within this framework. The discrete-time model in [8] is based on using multi-layer perceptron (MLP) networks to model the nonlinearities. While it may be difficult to use them to specify complex prior information, their functional form seems quite reasonable in many computational biology applications [6], for instance. The discrete-time state-space model studied in [8] assumes that the observations x(t) are generated by s(t + 1) = s(t) + gdt(s(t),θg) + m(t) (1)