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Minimum Stein Discrepancy Estimators
- A. Barp, François-Xavier Briol, A. Duncan, M. Girolami, Lester W. Mackey
- 19 June 2019
This work establishes the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, then derive stochastic Riemannian gradient descent algorithms for their efficient optimisation.
Statistical Inference for Generative Models with Maximum Mean Discrepancy
- François-Xavier Briol, A. Barp, A. Duncan, M. Girolami
- Computer Science, MathematicsArXiv
- 13 June 2019
Theoretical properties of a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intracted, but simulation is cheap, are studied, showing that they are consistent, asymptotically normal and robust to model misspecification.
Stein Point Markov Chain Monte Carlo
This paper removes the need to solve this optimisation problem by selecting each new point based on a Markov chain sample path, which significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement.
Metrizing Weak Convergence with Maximum Mean Discrepancies
It is shown that, on a locally compact, non-compact, Hausdorff space, the MMD of a bounded continuous Borel measurable kernel k, whose RKHS-functions vanish at infinity, metrizes the weak convergence of probability measures if and only if k is continuous and integrally strictly positive definite (ISPD) over all signed, finite, regular Borel measures.
A Riemannian-Stein Kernel method
This paper presents a theoretical analysis of numerical integration based on interpolation with a Stein kernel. In particular, the case of integrals with respect to a posterior distribution supported…
Stein’s Method Meets Statistics: A Review of Some Recent Developments
Stein’s method is a collection of tools for analysing distributional comparisons through the study of a class of linear operators called Stein operators. Originally studied in probability, Stein’s…
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.
A numerical study of the 3D random interchange and random loop models
We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The…
Hamiltonian Monte Carlo on Symmetric and Homogeneous Spaces via Symplectic Reduction
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the…
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. In this paper, we develop a geometric theory that…