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Found 21 papers, 10 papers with code
Sobolev Spaces, Kernels and Discrepancies over Hyperspheres
This work provides theoretical foundations for kernel methods in the hyperspherical context.
Generalised Bayesian Inference for Discrete Intractable Likelihood
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical.
Black Box Probabilistic Numerics
One approach is to model the unknown quantity of interest as a random variable, and to constrain this variable using data generated during the course of a traditional numerical method.
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied.
Robust Generalised Bayesian Inference for Intractable Likelihoods
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood.
Optimal quantisation of probability measures using maximum mean discrepancy
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i. e., to approximate a target distribution by a representative point set.
Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators.
Optimal Thinning of MCMC Output
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced.
Semi-Exact Control Functionals From Sard's Method
The numerical approximation of posterior expected quantities of interest is considered.
Computation Methodology
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model.
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.
Improved Calibration of Numerical Integration Error in Sigma-Point Filters
The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF.
Rejoinder for "Probabilistic Integration: A Role in Statistical Computation?"
This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?"
Symmetry Exploits for Bayesian Cubature Methods
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited.
Methodology Numerical Analysis Computation
Stein Points
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$.
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.
Causal Learning via Manifold Regularization
This paper frames causal structure estimation as a machine learning task.
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.
Exact Estimation of Multiple Directed Acyclic Graphs
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models.
