Related papers: Identification of Gaussian Process State Space Mod…

Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…

In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…

Planning is a powerful approach to control problems with known environment dynamics. In unknown environments the agent needs to learn a model of the system dynamics to make planning applicable. This is particularly challenging when the…

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

The ability to predict future states is crucial to informed decision-making while interacting with dynamic environments. With cameras providing a prevalent and information-rich sensing modality, the problem of predicting future states from…

Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates…