Related papers: Variational Gaussian Process Dynamical Systems

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…

We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized…

Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain…

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…

Recently, Gaussian Splatting methods have emerged as a desirable substitute for prior Radiance Field methods for novel-view synthesis of scenes captured with multi-view images or videos. In this work, we propose a novel extension to 4D…

Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The…

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…

Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

While optimal input design for linear systems has been well-established, no systematic approach exists for nonlinear systems where robustness to extrapolation/interpolation errors is prioritized over minimizing estimated parameter variance.…

The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…