Related papers: Inferring the unknown parameters in Differential E…
In this paper, we present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems affected by bounded disturbances and unmodeled nonlinearities. We use Gaussian Processes (GPs) to learn the uncertain…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
Stiff ordinary differential equations (ODEs) play an important role in many scientific and engineering applications. Often, the dependence of the solution of the ODE on additional parameters is of interest, e.g.\ when dealing with…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…
This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been…
Causal discovery and inference from observational data is an essential problem in statistics posing both modeling and computational challenges. These are typically addressed by imposing strict assumptions on the joint distribution such as…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…