Structured Variational Inference in Unstable Gaussian Process State Space Models

by   Silvan Melchior, et al.
ETH Zurich

Gaussian processes are expressive, non-parametric statistical models that are well-suited to learn nonlinear dynamical systems. However, large-scale inference in these state space models is a challenging problem. In this paper, we propose CBF-SSM a scalable model that employs a structured variational approximation to maintain temporal correlations. In contrast to prior work, our approach applies to the important class of unstable systems, where state uncertainty grows unbounded over time. For these systems, our method contains a probabilistic, model-based backward pass that infers latent states during training. We demonstrate state-of-the-art performance in our experiments. Moreover, we show that CBF-SSM can be combined with physical models in the form of ordinary differential equations to learn a reliable model of a physical flying robotic vehicle.


page 1

page 2

page 3

page 4


Probabilistic Recurrent State-Space Models

State-space models (SSMs) are a highly expressive model class for learni...

Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features

Effectively modeling phenomena present in highly nonlinear dynamical sys...

Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems

Probabilistic inference in high-dimensional state-space models is comput...

ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems

Parameter inference in ordinary differential equations is an important p...

Traversing Time with Multi-Resolution Gaussian Process State-Space Models

Gaussian Process state-space models capture complex temporal dependencie...

The Lévy State Space Model

In this paper we introduce a new class of state space models based on sh...

Φ-DVAE: Learning Physically Interpretable Representations with Nonlinear Filtering

Incorporating unstructured data into physical models is a challenging pr...

Code Repositories


Official implementation of the CBF-SSM model

view repo

Please sign up or login with your details

Forgot password? Click here to reset