arXiv research

2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.

Study continuity and Hölder estimates for solutions on Stein spaces.

Characterizes Stein surfaces with finite homotopy rank-sum.

Study on Hölder continuity of complex Monge-Ampère solutions on Stein spaces.

Paper solves CR positive mass and Yamabe problems on weighted spaces.

In this new version, we give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in $\mathbb{C}^n, n\geq 2,$ is Kähler-Einstein if and only if the domain is biholomorphic to the ball. We establish versions of various …

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of this technique is conducted for the previously unconsidered setting where samples…

A new method de-randomizes MCMC dynamics using the Stein operator.

Unbraided wiring diagrams for Stein fillings of lens spaces are described.

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…

Generalizes Nakano-positivity to Hilbert space fields.

The paper characterizes unit balls among Stein spaces with specific groups using Bergman-Einstein metrics.

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and …

Stein transport improves Bayesian inference with faster convergence and reduced variance.

We prove that if a contact manifold $(M,ξ)$ is supported by a planar open book, then Euler characteristic and signature of any Stein filling of $(M,ξ)$ is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein filli…

A new test assesses how well observed networks fit a specified ERGM model.

Paper analyzes SVGD algorithm for non-asymptotic convergence.

The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained --- they correspond to open handlebodies with all handles of index lessthan or = 2. An uncountable collection of exotic R^4's is shown to ad…

Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.

New samplers minimize KL divergence for constrained and non-Euclidean geometries.

A new kernel Stein test assesses fit for variable-length sequential data.

The paper computes a tau-invariant for holomorphic curves in Stein domains and links.

New definition of regular points for PL functions on manifolds.

Stein's method improves probabilistic inference and learning.

Classifies tight contact structures on surgeries of the Whitehead link.

BSVGD improves sampling for multimodal distributions using branching.

Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.

New method reduces computational cost for learning stationary diffusions.

A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others homotopy equivalent to the 2-sphere but cut out by smooth, compact 3-manifolds. …

The paper explores nonexistence and existence of symplectic and Stein fillable contact structures on 3-manifolds.

New research sets the minimax lower bound for KSD estimation at sqrt(n).

Improved kernel Stein discrepancy for large-scale data.

Stein variational neural network ensembles improve diversity and uncertainty estimation.

For a compact contact manifold it is shown that the anisotropic Folland-Stein function spaces form an algebra. The notion of anisotropic regularity is extended to define the space of Folland-Stein contact diffeomorphisms, which is shown to be a topological group under composition and a smooth Hilbert manifold. These re…

GC Stein manifolds characterized with embeddings and functions.

Stochastic Stein Discrepancies improve inference efficiency.

A new method for SVGD reduces variance in high dimensions.

We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected a…

Improved sampling method using regularized Stein Variational Gradient Flow.

Develops Stein's method for Riemannian manifolds using diffusion.

It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.

Regularized Stein thinning improves MCMC output approximations.

Study Stein and Milnor fillings of links from surface singularities.

Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either required strong technical assumptions or were limited to Gaussian distributions with …

The paper classifies symplectic fillings of lens spaces and constructs cobordisms.

In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most results pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map $X\to Y$ between Stein manifolds is homotopic to a proper holomorphic em…

In this article we give a sharp upper bound on the possible values of the Euler characteristic for a minimal symplectic filling of a tight contact structure on a lens space. This estimate is obtained by looking at the topology of the spaces involved, extending this way what we already knew from the universally tight ca…