Search Results for author:
Found 53 papers, 15 papers with code
Towards Multilevel Modelling of Train Passing Events on the Staffordshire Bridge
We formulate a combined model from simple units, representing strain envelopes (of each train passing) for two types of commuter train.
Improving embedding of graphs with missing data by soft manifolds
The reliability of graph embeddings directly depends on how much the geometry of the continuous space matches the graph structure.
Riemannian Laplace Approximation with the Fisher Metric
Laplace's method approximates a target density with a Gaussian distribution at its mode.
Warped geometric information on the optimisation of Euclidean functions
We use Riemannian geometry notions to redefine the optimisation problem of a function on the Euclidean space to a Riemannian manifold with a warped metric, and then find the function's optimum along this manifold.
Encoding Domain Expertise into Multilevel Models for Source Location
Most interestingly, domain expertise and knowledge of the underlying physics can be encoded in the model at the system, subgroup, or population level.
Inferring networks from time series: a neural approach
Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media.
Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation
We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables.
Random Grid Neural Processes for Parametric Partial Differential Equations
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes.
Sobolev Spaces, Kernels and Discrepancies over Hyperspheres
This work provides theoretical foundations for kernel methods in the hyperspherical context.
$Φ$-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation
To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder ($\Phi$-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations.
Neural parameter calibration for large-scale multi-agent models
Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time.
Targeted Separation and Convergence with Kernel Discrepancies
Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference.
Fully probabilistic deep models for forward and inverse problems in parametric PDEs
In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks.
Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making.
Lagrangian Manifold Monte Carlo on Monge Patches
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account.
A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection
This system provides several constraints and assumptions on the data properties that might be not valid for multimodal data analysis, especially when large scale datasets collected from heterogeneous sources are considered, so that the accuracy and robustness of the outcomes might be severely jeopardized.
Bayesian Learning via Neural Schrödinger-Föllmer Flows
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i. e. Schr\"odinger bridges).
Statistical Finite Elements via Langevin Dynamics
Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model.
Low-rank statistical finite elements for scalable model-data synthesis
Statistical learning additions to physically derived mathematical models are gaining traction in the literature.
Optimization on manifolds: A symplectic approach
Optimization tasks are crucial in statistical machine learning.
Enhancing ensemble learning and transfer learning in multimodal data analysis by adaptive dimensionality reduction
Nonetheless, when applied to multimodal datasets (i. e., datasets acquired by means of multiple sensing techniques or strategies), the state-of-theart methods for ensemble learning and transfer learning might show some limitations.
A Unifying and Canonical Description of Measure-Preserving Diffusions
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework.
Near Real-Time Social Distance Estimation in London
During the COVID-19 pandemic, policy makers at the Greater London Authority, the regional governance body of London, UK, are reliant upon prompt and accurate data sources.
Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests
The MF predictive uncertainty is also found to be better calibrated and less computationally costly than the uncertainty estimated from applying jackknifing to random forest predictions.
Fluid Dynamics Computational Physics
Semi-Exact Control Functionals From Sard's Method
The numerical approximation of posterior expected quantities of interest is considered.
Computation Methodology
Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness
In this setting, an important theoretical question of practial relevance is how accurate the Gaussian process approximations will be given the difficulty of the problem, our model and the extent of the misspecification.
Precision-Recall Balanced Topic Modelling
Topic models are becoming increasingly relevant probabilistic models for dimensionality reduction of text data, inferring topics that capture meaningful themes of frequently co-occurring terms.
Multi-resolution Multi-task Gaussian Processes
We consider evidence integration from potentially dependent observation processes under varying spatio-temporal sampling resolutions and noise levels.
Minimum Stein Discrepancy Estimators
We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths.
Statistical Inference for Generative Models with Maximum Mean Discrepancy
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges.
The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
From the outset, we postulate a data-generating model which additively decomposes data into a finite element, a model misspecification and a noise component.
Methodology Numerical Analysis Numerical Analysis
Stein Point Markov Chain Monte Carlo
Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point.
Efficiency and robustness in Monte Carlo sampling of 3-D geophysical inversions with Obsidian v0.1.2: Setting up for success
We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty, using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study.
Rejoinder for "Probabilistic Integration: A Role in Statistical Computation?"
This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?"
Posterior Inference for Sparse Hierarchical Non-stationary Models
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed.
Computation
A Bayesian Conjugate Gradient Method
The estimates obtained in this case are of little value unless further information can be provided about the numerical error.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
Bayesian Quadrature for Multiple Related Integrals
This allows users to represent uncertainty in a more faithful manner and, as a by-product, provide increased numerical efficiency.
Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation.
Applications
On the Sampling Problem for Kernel Quadrature
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the smoothness and dimension of the integrand.
Geometry and Dynamics for Markov Chain Monte Carlo
The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods.
Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
Hyperpriors for Matérn fields with applications in Bayesian inversion
We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors.
Statistics Theory Statistics Theory
Bayesian modelling and quantification of Raman spectroscopy
Raman spectroscopy can be used to identify molecules such as DNA by the characteristic scattering of light from a laser.
Applications Computation 92E99, 65D10, 62F15, 62H12
On the Geometric Ergodicity of Hamiltonian Monte Carlo
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic.
Probabilistic Integration: A Role in Statistical Computation?
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled.
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation.
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations.
Unbiased Bayes for Big Data: Paths of Partial Posteriors
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution.
Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters.
Methodology Statistics Theory Statistics Theory
Pseudo-Marginal Bayesian Inference for Gaussian Processes
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data.
On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data.
Analysis of SVM with Indefinite Kernels
The recent introduction of indefinite SVM by Luss and dAspremont [15] has effectively demonstrated SVM classification with a non-positive semi-definite kernel (indefinite kernel).
Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes
We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.
