Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.
problem Intractable likelihoods in Bayesian inference.
method Generalised Bayesian inference with Stein discrepancy as the loss function.
result Robust generalised posteriors with closed form or accessible using MCMC.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
Improved neural network ensembles using Stein Variational Newton updates.
problem Lack of efficient second-order information in current ensemble methods.
method Proposes a novel approximate Bayesian inference method integrating Stein Variational Newton updates with scalable Hessian approximations.
result Significantly faster convergence and more accurate posterior distribution approximations.
Improved kernel Stein discrepancy for large-scale data.
problem Efficiently testing probability distributions with kernel methods.
method Nyström approximation to reduce runtime complexity.
result Nyström-based KSD is n \sqrt{n} n -consistent and applicable for large datasets. New OLO algorithms use Stein's method for better performance tradeoffs.
problem Achieving optimal tradeoffs in adversarial online linear optimization.
method Operationalizing Stein's method for computationally efficient OLO algorithms.
result Additively sharp upper bounds on regret and total loss.
Burq-Gérard-Tzvetkov and Hu established L p L^p L p estimates ( 2 ≤ p ≤ ∞ 2\le p\le \infty 2 ≤ p ≤ ∞ ) for the restriction of eigenfunctions to submanifolds. The estimates are sharp, except for the log loss at the endpoint L 2 L^2 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.
problem Sampling from complex target distributions efficiently.
method Wasserstein gradient flow of KSD, using L-BFGS optimization.
result KSD Descent can sample from a target distribution using a set of particles.
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.
problem Improving probabilistic inference and learning methods.
method Constructing Stein discrepancies from Stein operators and Stein sets, discussing their properties.
result Connection between Stein operators and Stein variational gradient descent.
A new method improves Bayesian inference for multimodal posteriors.
problem Insensitivity to well-separated modes in multimodal posteriors.
method Weighted Kernel Stein Discrepancy method.
result Significantly improved mode sensitivity compared to standard KSD-Bayes.
Paper proves robust M-estimators' coordinates' normality in high dimensions.
problem High-dimensional robust M-estimators' asymptotic normality.
method Develops Stein formulae for high-dimensional random vectors on the sphere.
result Asymptotic normality holds for most coordinates of robust M-estimators with convex penalty.
SLOGAN improves GANs' conditional generation by balancing latent attribute distributions.
problem Imbalanced latent attribute distributions in GANs.
method Stein latent optimization with a Gaussian mixture prior and contrastive loss.
result SLOGAN achieves state-of-the-art unsupervised conditional generation performance.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L L L -plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L L L -plurisubharmonic exhaustion functions and GH embeddings. Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Paper proposes LSVGD to stabilize GAN training via Langevin Stein Variational Gradient Descent.
problem Mode collapse and performance deterioration in GAN training.
method Langevin Stein Variational Gradient Descent (LSVGD) incorporating noise to stabilize training.
result LSVGD improves performance and stability of various GAN models.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
problem Computing gradients for complex distributions with weak assumptions.
method Generalizes Stein's lemma to exponential-family mixtures and applies it to reparameterization trick.
result Derives new gradient identities for various distributions.
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.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
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.
problem Pathologies in Stein thinning leading to poor approximations.
method Theoretical analysis and regularization to improve KSD.
result Regularized Stein thinning alleviates pathologies and improves efficiency.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
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 → Y X\to Y X → Y between Stein manifolds is homotopic to a proper holomorphic em…
The paper improves Stein importance sampling for Markov chain samples.
problem Improving the accuracy of sampling from complex distributions.
method Reproducing Stein kernels approach for post-hoc correction.
result Consistent estimators for target distributions using geometrically ergodic Markov chains.
Counterexample found for Stein property of certain solvable Lie groups.
problem Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.
method Constructing a solvable Lie group with specific properties.
result A simply connected solvable Lie group with a left-invariant complex structure whose universal cover is not Stein.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
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.
problem Characterizing submanifolds with constant curvature in space forms.
method Analyzing submanifolds with flat normal connection or codimension 2.
result 2-stein submanifolds have constant curvature under specified conditions.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
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.
problem Slow and computationally intractable KSD tests.
method Nyström acceleration for KSD estimation.
result Asymptotic properties preserved by Nyström acceleration.
For any integer n ≥ 2 n\geq 2 n ≥ 2 , we construct an infinite family of Stein fillable contact ( 4 n − 1 ) (4n-1) ( 4 n − 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.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
Study continuity and Hölder estimates for solutions on Stein spaces.
problem Continuity and Hölder estimates for solutions to degenerate complex Monge-Ampère equations.
method Prove continuity up to the boundary and local Hölder estimates on the regular locus.
result Local Hölder estimates on the regular locus for solutions to degenerate complex Monge-Ampère equations.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
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…
Complete negative Kähler-Einstein metric found on Stein manifolds.
problem Existence of complete Kähler-Einstein metrics on Stein manifolds with negative curvature.
method Normalized Kähler-Ricci flow to deform metrics to complete negative Kähler-Einstein metric.
result Existence of complete negative Kähler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature.
Paper proves existence of compatible Lefschetz fibrations on 6-ball and Stein domains.
problem Existence of compatible Lefschetz fibrations on Stein domains.
method Topological proof for 6-ball fibrations, construction of relative Stein pairs.
result Existence of compatible Lefschetz fibrations on Stein domains of dimension six.
New Stein operator improves robustness in model inference.
problem Improving robustness in inference for unnormalized models.
method Density-power weighted Stein operator ( γ γ γ -Stein operator). result Robust methods for goodness-of-fit testing and posterior approximation.
Characterizes Stein surfaces with finite homotopy rank-sum.
problem Finite homotopy rank-sum in Stein spaces.
method Rational homotopy theory, classification of Stein surfaces.
result Affine Stein surfaces with finite fundamental group are either simply connected or of order 2.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.
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.
problem High-dimensional integration inefficiency in flow matching.
method Density-weighted Dynamic Stein operators.
result Significant improvement in vector field smoothness and sampling efficiency.
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…