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Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…

Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

Due to the increasing complexity of technical systems, accurate first principle models can often not be obtained. Supervised machine learning can mitigate this issue by inferring models from measurement data. Gaussian process regression is…

Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…

Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying…

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…

Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then…

This paper proposes a novel framework for implicit multi-camera system calibration utilizing Gaussian Process (GP) regression. Conventional explicit calibration methods are constrained by rigid mathematical models and struggle with complex,…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…