arXiv research

New Stein Points use Markov chains to select points, reducing computational cost.

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 $\{x_i\}_{i=1}^n$. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achi…

Develops Stein's method for Riemannian manifolds using diffusion.

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

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

New definition of regular points for PL functions on manifolds.

New compression methods handle biased input sequences for more accurate posterior summaries.

Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of functions, which we call the Stein matching set, whose expectations are exactly …

A new sequential test for unnormalized densities.

Improved kernel Stein discrepancy for large-scale data.

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

There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is shown that, even though …

A new method for Bayesian inference in high dimensions using projected Stein variational gradient descent.

Stein's method improves probabilistic inference and learning.

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target dist…

GC Stein manifolds characterized with embeddings and functions.

Stochastic Stein Discrepancies improve inference efficiency.

Extends Stein's lemma to exponential-family mixtures for gradient computation.

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.

Regularized Stein thinning improves MCMC output approximations.

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

Study Stein and Milnor fillings of links from surface singularities.

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

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…

The paper improves Stein importance sampling for Markov chain samples.

Counterexample found for Stein property of certain solvable Lie groups.

A new framework improves kernel Stein discrepancy tests for validating distributions.

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…

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifo…

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

New KCC-SDs improve distribution comparison in high dimensions.

Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention …

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study continuity and Hölder estimates for solutions on Stein spaces.

Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing

Complete negative Kähler-Einstein metric found on Stein manifolds.

Paper proves existence of compatible Lefschetz fibrations on 6-ball and Stein domains.

New Stein operator improves robustness in model inference.

Characterizes Stein surfaces with finite homotopy rank-sum.

A new method reduces complexity and uncertainty in neural networks.

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 …

We characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. We also show that for this class of 3-manifolds the existence of Stein fillings is equivalent to the existence of symplectic fillings.

A unified summary is given of the existence theory of Stein manifolds in all dimensions, based on published and pending literature. Eliashberg's characterization of manifolds admitting Stein structures requires an extra delicate hypothesis in complex dimension 2, which can be eliminated by passing to the topological se…