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Found 13 papers, 2 papers with code
Deep Learning as Ricci Flow
To illustrate this idea, we present a computational framework to quantify the geometric changes that occur as data passes through successive layers of a DNN, and use this framework to motivate a notion of `global Ricci network flow' that can be used to assess a DNN's ability to disentangle complex data geometries to solve classification problems.
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.
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.
Controlling Moments with Kernel Stein Discrepancies
Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant.
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.
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.
Optimization on manifolds: A symplectic approach
Optimization tasks are crucial in statistical machine learning.
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.
Metrizing Weak Convergence with Maximum Mean Discrepancies
More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD of a bounded continuous Borel measurable kernel k, whose reproducing kernel Hilbert space (RKHS) functions vanish at infinity, metrizes the weak convergence of probability measures if and only if k is continuous and integrally strictly positive definite (i. s. p. d.)
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.
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.
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.
