arXiv research

Stein's method improves probabilistic inference and learning.

Develops Stein's method for Riemannian manifolds using diffusion.

Improved sampling method using regularized Stein Variational Gradient Flow.

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 …

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…

A new method reduces complexity and uncertainty in neural networks.

Adapts Stein's method for geometric inequalities, addressing boundary terms.

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

New Stein operator improves robustness in model inference.

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

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

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

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…

A simple method constructs Lefschetz fibrations on compact Stein surfaces.

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and …

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…

Improved kernel Stein discrepancy for large-scale data.

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

In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from convex surface theory and classifications of tight contact structures on certain 3-m…

Improved neural network ensembles using Stein Variational Newton updates.

SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.

Stein discrepancy improves UDA performance in low-data scenarios.

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

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…

GC Stein manifolds characterized with embeddings and functions.

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

Stochastic Stein Discrepancies improve inference efficiency.

New method uses multiple kernels to improve SVGD performance.

Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.

We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of functional gradient descent that minimizes the KL divergence. Empirical studies…

A conjecture due to Gompf asserts that no nontrivial Brieskorn homology sphere admits a pseudoconvex embedding in ${\mathbb C}^2$, with either orientation. A related question asks whether every compact contractible 4-manifold admits the structure of a Stein domain. We verify Gompf's conjecture, with one orientation, fo…

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

BSVGD improves sampling for multimodal distributions using branching.

Paper proposes approximate Stein classes for efficient truncated density estimation.

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.

We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly de…

Study Stein and Milnor fillings of links from surface singularities.

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…

Paper proposes kernelized Stein tests for time-to-event data with censoring.

Counterexample found for Stein property of certain solvable Lie groups.

Bayesian online changepoint detection (BOCPD) (Adams & MacKay, 2007) offers a rigorous and viable way to identify changepoints in complex systems. In this work, we introduce a Stein variational online changepoint detection (SVOCD) method to provide a computationally tractable generalization of BOCPD beyond the exponent…

Stein-Encoder isolates genetic signals in multi-modal biomedical data.

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

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

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…

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

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…