arXiv research

Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging indications on the effectiveness of the method. An application to density-based c…

Improved OOD detection using label smoothing and k-NN density estimates.

Survey on smooth function and form density in Riemannian Sobolev spaces.

Most density-based clustering methods largely rely on how well the underlying density is estimated. However, density estimation itself is also a challenging problem, especially the determination of the kernel bandwidth. A large bandwidth could lead to the over-smoothed density estimation in which the number of density …

On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher--Rao metric.

Paper proposes new density estimators for high-dimensional data.

Optimizes spectral density estimation for stationary and nonstationary processes.

Generative models improved with smoothed score functions for better sample quality.

A boosting method improves nonparametric density estimation without smoothing assumptions.

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of th…

SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.

New statistical framework for coresets in density estimation.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

Develops a new test for comparing two groups' densities, showing minimax optimality.

The Riemannian Langevin Algorithm samples from manifolds efficiently.

The paper analyzes kNN density estimation's convergence rates under different conditions.

New method efficiently interpolates nonparametric density estimators.

Improved MLMC method for robust and efficient probability and density estimation.

We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in the ring of normal densities on a manifold.

We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Has…

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding the $L^2$-Wasserstein distance of optimal mass transport, and the Fisher--Rao me…

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.

New method improves counterfactual distribution learning for high-dimensional outcomes.

Optimizes graph spectral density learning for large networks.

Method estimates densities on manifolds using dequantization.

It is known that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive densities that is invariant under the action of the diffeomorphism group, is of the form $G_μ(α,β)=C_1(μ(M)) \int_M \fracαμ\fracβμ\,μ+ C_2(μ(M)) \int_Mα\cdot \int_Mβ$ for some smoo…

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific …

Adaptive kernel density estimation improves accuracy in high dimensions.

High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.

A model-free framework extracts risk-neutral densities from short-dated options.

Interactive privacy mechanisms improve spectral density estimation under local differential privacy.

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…

The COS method for European options pricing is improved with a new bound for the number of terms.

The study finds anisotropic minimal surfaces in 3-manifolds with smooth boundaries.

MALA mixes efficiently under smoothness and isoperimetry assumptions.

Proves stability of cone-volume measure with nearly constant density.

The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF). A diffeomorphic flow is an invertible function where both the function and its i…

Efficiently clusters large datasets using low-density hyperplanes.

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the regression function is smooth over high-density clusters or manifolds supporting the dat…

Unified smoothing for robust classification improves accuracy.

Generic metrics make geodesic nets dense.

We study in this paper the rate of convergence for learning densities under the Generative Adversarial Networks (GAN) framework, borrowing insights from nonparametric statistics. We introduce an improved GAN estimator that achieves a faster rate, through simultaneously leveraging the level of smoothness in the target d…

The paper introduces new estimators for multivariate functions using Fourier methods.

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the unique compact, orientable, second order minima of the weighted area under variation…

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…

Estimates nonparametric densities from mixed samples.

Entire area-minimizing surfaces of density 2 are planar or quadratic

New method combines strengths of two PCL approaches without density ratio estimation.