arXiv research

Fast approximate inference for non-Gaussian data.

This study examines the practical equivalence of Laplace and neural tangent kernels.

Improved bounds for estimating discrete distributions in KL divergence.

A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.

Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propag…

A new method matches similar regions in non-rigid shapes using spectra of differential operators.

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalize…

A scalable method for Bayesian inference in large linear models.

We show that if two closed hyperbolic surfaces (not necessarily orientable or even connected) have the same Laplace spectrum, then for every length they have the same number of orientation-preserving geodesics and the same number of orientation-reversing geodesics. Restricted to orientable surfaces, this result reduces…

Improved regret bounds for DP-KLUCB and DP-IMED in Bernoulli bandits.

The paper analyzes rates of approximation for eigenpairs of Laplace-Beltrami operators on manifolds.

Let $x : M \to E^m$ be an isometric immersion of a Riemannian manifold $M$ into a Euclidean $m$-space. Denote by $Δ$ the Laplace operator of $M$. Then $Δ$ gives rise to a differentiable map $L :M \to E^m$, called the Laplace map, defined by $L(p)=(Δx)(p)$, $p\in M$. We call $L(M)$ the Laplace image, and the transformat…

The paper examines special Q-nets that terminate after a finite number of Laplace steps.

Paper improves parameter estimation of continuous distributions using preference feedback.

Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.

Introduces a new elliptic operator with positive eigenvalue.

Revisits online Laplace methods for neural networks, showing they are sound under certain conditions.

Trapezoids uniquely identified by their Dirichlet Laplace spectrum.

Formula derived for Laplace-Beltrami on Stiefel manifold.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

New methods improve Laplace approximations for deep neural networks by selecting key parameters.

A new method combines Laplace and Variational Bayes for scalable inference.

The paper studies graph Laplace operator behavior near isolated singularities.

QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.

Geometrically reformulates the Laplace method for optimal transport.

MCMC complexity matches optimization for large $n$ and $d$.

Study finds metrics maximizing one Laplace eigenvalue on 3D and higher manifolds.

Neural Laplace models diverse DEs in the Laplace domain for better dynamics.

Graph Laplace operators uniquely identify metrics and densities on manifolds.

The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All of the Laplace opera…

The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds. Stre…

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve…

We prove inequalities for Laplace eigenvalues of Kaehler manifolds generalising to higher eigenvalues the classical inequality for the first Laplace eigenvalue due to Bourguignon, Li, and Yau in 1994. We also obtain similar inequalities for analytic varieties in Kaehler manifolds.

Variational Laplace improves Bayesian neural networks performance.

The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Lap…

Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.

Improved spectral convergence bounds for diffusion maps on tori.

Variational Laplace improves Bayesian neural network performance without sampling.

This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.

Paper studies Laplace operator estimates in harmonic map heat flows.

Study bounds the measure of zero sets of Neumann Laplace eigenfunctions.

Method finds domain of Laplace-Beltrami operator on 2D almost-Riemannian manifolds.

Study the smallest Laplace eigenvalue in special geometric spaces.

Paper introduces Laplace-HDC for better binary hyperdimensional computing.

The problem of learning a correspondence relationship between nodes of two networks has drawn much attention of the computer science community and recently that of statisticians. The unseeded version of this problem, in which we do not know any part of the true correspondence, is a long-standing challenge. For low-rank…

The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.