9 papers
Hierarchical Bayesian Quadrature
Tim Weiland, Toni Karvonen, Philipp Hennig
Numerical integration is a cornerstone of various scientific computing applications, such as engineering simulations and model evidence computations in probabilistic machine learni…
Scalable Bayesian Inference for Nonlinear Conservation Laws
Tim Weiland, Philipp Hennig
Nonlinear conservation laws are at the heart of many of the most important dynamical systems in science and engineering. In practical applications, such systems are often subject t…
Conditioning Gaussian Processes on Almost Anything
Henry Moss, Lachlan Astfalck, Thomas Cowperthwaite +5
Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalenc…
Sample Path Regularity of Gaussian Processes from the Covariance Kernel
Nathaël Da Costa, Marvin Pförtner, Lancelot Da Costa +1
Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive unders…
Computation-Aware Kalman Filtering and Smoothing
Marvin Pförtner, Jonathan Wenger, Jon Cockayne +1
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with…
Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields
Tim Weiland, Marvin Pförtner, Philipp Hennig
Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilisti…