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Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…
A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the…
Many algorithms have been developed to estimate probability distributions subject to differential privacy (DP): such an algorithm takes as input independent samples from a distribution and estimates the density function in a way that is…
Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…
We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
Branches swaying in the breeze, flags rippling in the wind, and boats rocking on the water all show how aerodynamics shape natural motion -- an effect crucial for realism in vision and graphics. In this paper, we present Gaussian Swaying, a…
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation, Gaussian smoothing and smoothing on a sphere. The methods…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error…
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via $L_2$…
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
Learning multiple tasks sequentially requires neural networks to balance retaining knowledge, yet being flexible enough to adapt to new tasks. Regularizing network parameters is a common approach, but it rarely incorporates prior knowledge…
We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic…