Related papers: Kriging via variably scaled kernels
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…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel…
Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning…
This work develops a multivariate extension of the Fixed Rank Kriging (FRK) framework for spatial prediction in settings where multiple spatial processes may provide complementary information. The goal is to preserve the computational…
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…
Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…
Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…
In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…
As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP…
Standard kernels such as Mat\'ern or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more…
Motivated by the need for efficient and personalized learning in mobile health, we investigate the problem of online kernel selection for Gaussian Process regression in the multi-task setting. We propose a novel generative process on the…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
We investigate the capabilities and limitations of Gaussian process models by jointly exploring three complementary directions: (i) scalable and statistically efficient inference; (ii) flexible kernels; and (iii) objective functions for…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…