Related papers: Multi-fidelity modeling with different input domai…
Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…
This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems, so called recurrent models are frequently used. In this paper…
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…
We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational)…
Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process…
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…
Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…
Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…
Highly accurate numerical or physical experiments are often time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide…
Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…
Reliable uncertainty estimates are crucial in modern machine learning. Deep Gaussian Processes (DGPs) and Deep Sigma Point Processes (DSPPs) extend GPs hierarchically, offering promising methods for uncertainty quantification grounded in…
The increasing availability of high-dimensional, longitudinal measures of gene expression can facilitate understanding of biological mechanisms, as required for precision medicine. Biological knowledge suggests that it may be best to…
Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…
Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…
Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have…