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.
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.
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.
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 improves Stein property for certain Kahler manifolds.
problem Complete open Kahler manifolds with positive bisectional curvature being Stein.
method Restricts volume growth condition to a weaker one.
result Improves previous observation on Stein property.
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 …
We determine topological properties of Stein domains with boundary diffeomorphic to T^3, S^1\times S^2 and some Seifert fibered 3-manifolds.
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.
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…
Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.
problem Bayesian inference and Markov chain Monte Carlo methods.
method Stein variational gradient descent (SVGD) with deterministic and stochastic dynamics.
result Identifies Stein-Fisher information as the leading order contribution in the long-time and many-particle regime.
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.
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.
A new test assesses how well observed networks fit a specified ERGM model.
problem Testing the goodness of fit for ERGMs with a single network observation.
method Kernel Stein discrepancy combined with a discrete Stein operator for ERGMs, Monte Carlo simulation.
result The test provides theoretical and practical support for assessing ERGM fit.
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.
New Stein operator improves robustness in model inference.
problem Improving robustness in inference for unnormalized models.
method Density-power weighted Stein operator (γ-Stein operator). result Robust methods for goodness-of-fit testing and posterior approximation.
Clarifies properties of Ozsvath-Szabo contact invariant.
problem Properties and functoriality of Ozsvath-Szabo contact invariant.
method Explains and proves functoriality properties of the invariant.
result Strong functoriality under Stein cobordisms.
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
This paper analyzes Stein variational gradient descent for Bayesian inference.
problem Sampling or approximating high-dimensional probability distributions.
method Iterated steepest descent steps with a reproducing kernel Hilbert space norm.
result Performance gains of certain nondifferentiable kernels with adjusted tails.
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.
Study on curvature properties and Shafarevich conjecture for complex hyperbolic manifolds.
problem Existence and nonexistence of Kähler metrics with nonpositive curvature on toroidal compactifications.
method Analysis of toroidal compactifications of finite volume complex hyperbolic manifolds, verification of Shafarevich conjecture.
result Verification of Shafarevich conjecture for compactifications of quotients of complex hyperbolic space by non-uniform arithmetic lattices.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
Unified perspective on score matching and new estimators designed.
problem Infeasibility of maximum likelihood estimation in complex models.
method Minimum Stein discrepancy estimators, diffusion kernel Stein discrepancy (DKSD), diffusion score matching (DSM).
result Consistency, asymptotic normality, and robustness of DKSD and DSM estimators.
Stein shrinkage improves BN robustness against adversarial attacks.
problem Improving BN robustness against adversarial attacks.
method Applying Stein shrinkage to BN mean and variance estimates.
result Stein shrinkage outperforms vanilla BN in adversarial settings.
In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology 3-sphere supported by an open book decomposition with page a 4-holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillin…
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.
New method constructs Stein surfaces using topological isotopy.
problem Creating Stein surfaces in complex surfaces.
method Combining Freedman's topology with Eliashberg's holomorphic theory.
result Every tame 2-complex can be isotoped to a Stein surface.
A new method for Bayesian inference in high dimensions using projected Stein variational gradient descent.
problem Bayesian inference challenges in high-dimensional data.
method Adapting Stein variational gradient descent to exploit intrinsic low dimensionality of data.
result pSVGD is more accurate and efficient than SVGD, especially in high-dimensional settings.
The paper classifies and studies symplectic and contact properties of circular spherical divisors.
problem Investigating symplectic and contact topology of circular spherical divisors.
method Classification and analysis of concave circular spherical divisors, including embedding, Stein fillability, and rational homology type determination.
result All concave circular spherical divisors up to toric equivalence are realized as symplectic log Calabi-Yau pairs with minimal complements.
The study shows examples of contact 3-manifold binding sums that fail to preserve certain properties.
problem Examples of contact 3-manifold binding sums that fail to preserve properties like tightness or symplectic fillability.
method Examples and proofs of vanishing Heegaard Floer contact invariant for Stein fillable manifolds.
result Binding sums of contact 3-manifolds do not preserve properties such as tightness or symplectic fillability.
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
New class of complex manifolds defined, properties studied.
problem Understanding properties of complex manifolds.
method Introduced and studied wHHR manifolds, proved metric equivalence.
result Bergman and Kobayashi metrics are biLipschitz equivalent for wHHR Stein manifolds.
An isolated complex surface singularity induces a canonical contact structure on its link. In this paper, we initiate the study of the existence problem of Stein cobordisms between these contact structures depending on the properties of singularities. As a first step we construct an explicit Stein cobordism from any co…
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-o…
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.
Proposes a method to stabilize Black Box Variational Inference using the James-Stein estimator.
problem Stability issues and fine-tuning required in basic Black Box Variational Inference.
method Reframe stochastic gradient ascent as multivariate estimation problem using James-Stein estimator.
result Provides a simpler method with consistent performance in terms of model fit and convergence time.
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-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. Ad-SVGD optimizes kernel parameters for SVGD, improving inference performance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method Adaptive kernel selection for SVGD dynamics.
result Ad-SVGD outperforms standard heuristics in various tasks.
It is known that there is a unique concordance class in the free homotopy class of S1×pt⊂S1×S2. The constructive proof of this fact is given by the second author. It turns out that all the concordances in this construction are invertible. The knots K⊂S1×S2 with hyperbolic …
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…
Stein variational neural network ensembles improve diversity and uncertainty estimation.
problem Lack of proper Bayesian justification and diversity guarantees in deep neural network ensembles.
method Particle-based inference methods, specifically Stein variational gradient descent (SVGD), operating in weight space, function space, and hybrid settings.
result SVGD methods improve diversity and uncertainty estimation, approaching the true Bayesian posterior more closely.
Framework for accelerated gradient flows in Bayesian inverse problems.
problem Design efficient MCMC algorithms for Bayesian inverse problems.
method Nesterov's accelerated gradient flows in probability space, considering various information metrics.
result Proved convergence properties and proposed sampling-efficient algorithms for different metrics.
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 $\C$.
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.
Unified view of score estimators for flexible densities.
problem Estimating the score from unknown distributions.
method Regularized nonparametric regression framework.
result Unified convergence analysis and new estimators with desirable properties.
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 between Stein manifolds is homotopic to a proper holomorphic em…