arXiv research

Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.

Paper proves conditions for estimating precision matrices with Laplacian constraints.

Improved neural network ensembles using Stein Variational Newton updates.

Improved kernel Stein discrepancy for large-scale data.

New OLO algorithms use Stein's method for better performance tradeoffs.

Burq-Gérard-Tzvetkov and Hu established $L^p$ estimates ($2\le p\le \infty$) for the restriction of eigenfunctions to submanifolds. The estimates are sharp, except for the log loss at the endpoint $L^2$ estimates for submanifolds of codimension 2. It has long been believed that the log loss at the endpoint can be remov…

KSD Descent uses KSD to sample from a target distribution efficiently.

We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the data/distribution-dependent Efron-Stein (ES) estimate of its variance and they do not requ…

Stein's method improves probabilistic inference and learning.

A new method improves Bayesian inference for multimodal posteriors.

Paper proves robust M-estimators' coordinates' normality in high dimensions.

SLOGAN improves GANs' conditional generation by balancing latent attribute distributions.

GC Stein manifolds characterized with embeddings and functions.

Stochastic Stein Discrepancies improve inference efficiency.

Paper proposes LSVGD to stabilize GAN training via Langevin Stein Variational Gradient Descent.

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 …

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.

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…

Improved KSD test for faster GoF testing.

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.

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

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

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…

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 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.

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 …

A new method improves flow matching by dynamically weighting density estimates.

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…

For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented smo…