arXiv research

New Stein operator improves robustness in model inference.

Stein's method improves probabilistic inference and learning.

The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.

Stochastic Stein Discrepancies improve inference efficiency.

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…

The paper studies symplectic operations on Stein fillings of Brieskorn singularities.

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

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

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

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

Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…

Study eigenvalues and functions on specific Heisenberg manifolds.

AgraSSt assesses graph generators using Stein operators and kernel discrepancies.

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

CSD improves goodness-of-fit testing for higher-order dependence.

Develops Stein's method for Riemannian manifolds using diffusion.

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

SteinGen generates diverse graph samples from a single example.

Paper analyzes SVGD algorithm for non-asymptotic convergence.

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 …

Stein shrinkage improves BN robustness against adversarial attacks.

Extends Rothschild-Stein lifting method to non-nilpotent Lie algebras.

Improved kernel Stein discrepancy for large-scale data.

This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slovák has classified all conformally invariant differential operators on locally conformally flat manifolds. We complete his results in higher spin theory by giving explicit expressions for …

Bayesian neural networks speed up numerical integration.

StAD predicts divergence of diffusion and flow models without Jacobian computation.

Paper proposes a new method to assess synthetic data generators.

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-Röllin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition of Reinert-Röllin allows for wider applicability of the method, while the method of…

NOVI improves deep Gaussian process inference with neural generators and regularized Stein discrepancy.

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operator…

Improves gradient estimation for discrete distributions with variance reduction techniques.

Stein variational neural network ensembles improve diversity and uncertainty estimation.

We give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). We construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explic…

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

New Stein fillings found for non-weighted homogeneous singularities.

GC Stein manifolds characterized with embeddings and functions.

Fourier representation improves KSD for infinite-dimensional data.

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $Ω$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR em…

We prove that the total CR $Q$-curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the $P^\prime$-operator and the CR invariance of the total $Q^\prime$-curvature for any pseudo-Einstein manifold without the assumption that it bounds a Stein manifold.

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.

The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we first provide a decomposition of the higher spin Laplace operator in terms of Rr…

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 …