Combines local and global smoothing for multivariate density estimation.
problem Non-parametric multivariate density estimation.
method Combines local and global smoothing techniques.
result Simulation shows effectiveness of the method.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “smooth densities”
D-NND clusters by learning density layers, avoiding over- and under-smoothing.
problem Challenges in density-based clustering, especially bandwidth determination.
method Hierarchical density learning through Deep Nearest Neighbor Descent.
result Avoids over- and under-smoothing, discovers underlying cluster structure reliably.
New integral-geometric formulae derived from normal densities ring.
problem Smooth versions of BKK theorem.
method Algorithm based on ring of normal densities.
result Smooth versions of BKK theorem obtained.
Improved OOD detection using label smoothing and k-NN density estimates.
problem Detecting out-of-distribution examples in classification models.
method Label smoothing and k-NN density estimate on intermediate activations.
result Label smoothing improves OOD detection performance, both theoretically and empirically.
The Fisher-Rao metric on smooth densities is studied on compact manifolds.
problem Characterizing the Fisher-Rao metric on smooth densities.
method Analyzing geodesics, curvature, and completeness of the Fisher-Rao metric.
result Geodesics and curvature of the Fisher-Rao metric are determined.
Survey on smooth function and form density in Riemannian Sobolev spaces.
problem Density of smooth functions and forms in Sobolev spaces on Riemannian manifolds.
method Careful examination of weak covariant derivatives and partial derivatives.
result Equivalence of weak covariant derivatives to weak partial derivatives.
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.
problem Prohibitive computational cost and slow convergence rate in high-dimensional density estimation.
method Adaptive hyperbolic cross density estimators in mixed smooth Sobolev spaces.
result Proposed estimators do not suffer curse of dimensionality under Integral Probability Metrics.
Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processesstat.ME
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Generative models improved with smoothed score functions for better sample quality.
problem Improving generative models for better sample quality.
method Smoothed score functions based on factorial Gaussian kernels.
result Single noise level achieved 14.15 Fréchet inception distance on CIFAR-10.
Geodesic completeness for Riemannian metrics on smooth probability densities is studied.
problem None of the studied Riemannian metrics are geodesically complete.
method Analysis of Hamilton--Jacobi-like partial differential equations, providing order conditions for global existence and uniqueness.
result Geodesic completeness is established for a class of higher-order Sobolev type metrics.
Paper addresses bias in kernel density estimation under minimal assumptions.
problem Kernel density estimation bias under minimal assumptions.
method Demonstrates the need for a balance between kernel decay and bandwidth eigenvalues, and rigorously derives bias bounds.
result Explicit constants and rigorous derivation of bias bounds under minimal assumptions.
A boosting method improves nonparametric density estimation without smoothing assumptions.
problem Overfitting in nonparametric data fitting.
method Introduces a boosting algorithm for univariate nonparametric maximum likelihood estimation.
result Demonstrates the effectiveness of the boosting approach through simulations and real data experiments.
A Fourier transform approach optimizes clustering algorithms.
problem Optimizing clustering algorithms for accuracy and reliability.
method Fourier transform and Gaussian filtering to smooth density functions, detecting peaks as cluster centroids.
result Remarkable accuracy in finding cluster centroids, overcoming initialization problems.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
New statistical framework for coresets in density estimation.
problem Improving computational efficiency in density estimation.
method Developed a statistical framework for coresets in nonparametric density estimation.
result Practical coreset kernel density estimators are near-minimax optimal.
Improved GAN estimator learns densities faster with insights from nonparametric statistics.
problem How well GAN learns densities under different smoothness properties.
method Improved GAN estimator that leverages the level of smoothness and evaluation metric.
result Achieves a faster rate of convergence and near optimal minimax lower bound in high dimensions.
New inequalities link probability density norms to Sobolev norms and Kantorovich distances.
problem Bounding probability density norms on smooth weighted Riemannian manifolds.
method Refining and generalizing interpolation inequalities under condition.
result Established new inequalities linking norms to Sobolev norms and Kantorovich distances.
The paper analyzes a density estimator with exponential concentration.
problem Estimating integral functionals of continuous probability densities.
method Plug-in estimator for Hölder smooth densities on .
result The estimator converges at rate $O \left( n^{-\fracβ{β+ d}}
ight)$ and is exponentially concentrated.
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
problem Data on unknown manifolds without boundaries.
method Finite sample bounds and asymptotic normality for kernel smoothing and its derivatives.
result Established finite sample bounds and asymptotic normality for kernel smoothing.
Develops a new test for comparing two groups' densities, showing minimax optimality.
problem Comparing probability densities between two groups.
method Probabilistic tensor product smoothing spline framework for joint density modeling; penalized likelihood ratio test for interaction testing.
result Proposed test is minimax optimal and outperforms conventional approaches.
The Riemannian Langevin Algorithm samples from manifolds efficiently.
problem Sampling from distributions on manifolds with log-Sobolev inequality.
method Riemannian Langevin Algorithm, log-Sobolev inequality, self-concordance extension, stochastic smoothness bounding.
result The Riemannian Langevin Algorithm converges rapidly to the target density.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
New method efficiently interpolates nonparametric density estimators.
problem Efficient evaluation of nonparametric density estimators.
method Piecewise multivariate polynomial interpolation scheme.
result New estimator with low space requirements and efficient querying.
Improved MLMC method for robust and efficient probability and density estimation.
problem Stability and poor complexity of MLMC for low-regularity functionals.
method Numerical smoothing combined with MLMC for deterministic quadrature methods.
result Significant improvement in strong convergence and robustness of MLMC method.
New algorithm samples efficiently from complex composite potentials.
problem Sampling from densities with smooth and non-smooth components.
method Metropolis-Hastings framework with proximal-based proposal.
result Mixes to target density in iterations.
Novel active learning algorithm with improved convergence rate under local smoothness condition.
problem Improving convergence rates in active learning under specific smoothness assumptions.
method Developed a novel active learning algorithm with a rate of convergence better than in passive learning, using a local smoothness assumption for k-nearest neighbors.
result The algorithm achieves a better convergence rate than passive learning algorithms, avoiding strong density assumptions.
A new type of diffeomorphic normalizing flow for flexible density estimation.
problem Flexible density estimation and variational inference.
method Constructs a diffeomorphic flow using an ODE with a neural network to parametrize the smooth vector field and a recursive neural network for approximating the solution.
result End-to-end trained DDNF achieves competitive results on density estimation and variational inference tasks.
New method improves counterfactual distribution learning for high-dimensional outcomes.
problem Counterfactual distribution learning for high-dimensional outcomes with concentrated structure.
method Geometry-adaptive diffusion-guided smoothing estimators combining causal nuisance adjustment and local outcome geometry.
result Geometry-adaptive methods show steeper error decay in semi-synthetic experiments.
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.
Paper analyzes KSG mutual information estimator for smooth distributions.
problem Analyzing the convergence rate of KSG estimator for smooth distributions.
method Adaptive recombination of KL entropy estimators analysis.
result Convergence rate of KSG estimator for smooth distributions is analyzed.
Optimizes graph spectral density learning for large networks.
problem Ad-hoc kernel function and bandwidth selection in graph spectral techniques.
method Maximum Entropy approach to learn a smooth graph spectral density.
result Outperforms comparable iterative spectral approaches on synthetic and real graphs.
Method estimates densities on manifolds using dequantization.
problem Estimating densities on non-Euclidean manifolds.
method Inspired by dequantization, coordinate transformation, and normalizing flows.
result Successfully models densities on spheres, tori, and orthogonal groups.
Adaptive kernel density estimation improves accuracy in high dimensions.
problem Challenges in high-dimensional density estimation with traditional methods.
method Pre-training a neural network to recommend location-adaptive kernels.
result Effective density estimation in high dimensions with improved accuracy.
High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.
problem Training score-based generative models on complex, low-dimensional manifolds.
method Proves optimal rates for SGMs on smooth manifolds, separating into noise regimes and using ReLU nearest-projection coordinates.
result Optimal intrinsic Wasserstein rates are achieved, with polynomial ambient dependence for families with controlled geometry and density.
From Arbitrage Removal to Density Extraction: A Model-Free Framework for Short-Dated Optionsq-fin.CP
A model-free framework extracts risk-neutral densities from short-dated options.
problem Arbitrage and bid-ask spread issues in short-dated options.
method Develops ARIES for filtering static arbitrage and SEDEx for density extraction.
result Robust density extraction across various market conditions and volatility smiles construction.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
Unification of field theory and maximum entropy methods for learning probability densitiesphysics.data-an
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.
problem Determining the optimal number of terms in the COS method for accurate European option pricing.
method Using Fourier-cosine expansion, the study finds an explicit bound for the number of terms N in the cosine series approximation.
result The COS method achieves exponential convergence when the log-return density is smooth, but not when it has heavy tails.
The study finds anisotropic minimal surfaces in 3-manifolds with smooth boundaries.
problem Finding smooth anisotropic minimal surfaces in closed 3-manifolds.
method Min-max construction with elliptic integrands, uniform upper bound for density ratios.
result Obtains a smooth anisotropic minimal surface in a closed 3-manifold.
MALA mixes efficiently under smoothness and isoperimetry assumptions.
problem Sampling from target densities efficiently.
method Metropolis-Adjusted Langevin algorithm (MALA) with smoothness and isoperimetry assumptions.
result MALA mixes in $O\left(\frac{(LΥ)^{\frac12}}{ψ_μ^2} \log\left(\frac{1}ε
ight)
ight)$ iterations.
Proves stability of cone-volume measure with nearly constant density.
problem Stability of cone-volume measure with near constant density.
method Proves stability of cone-volume measure with near constant density.
result Homothetic copy of the body is close to the unit ball in the -distance.
Efficiently clusters large datasets using low-density hyperplanes.
problem Clustering large datasets efficiently.
method Incremental estimation of low-density hyperplanes using stochastic gradient descent.
result The method automatically selects an appropriate number of clusters.
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.
problem Improving robustness of classifiers against adversarial attacks.
method Learned smoothed densities and randomized smoothing.
result Provable robust accuracies higher than state-of-the-art defenses.
A new model sHDP adds smoothness constraints to HDP for evolving mixture densities.
problem Evolution of mixture densities in time-varying scenarios.
method Smoothed Hierarchical Dirichlet Process (sHDP) with temporal constraints.
result Inference algorithm and experimental validation on NIPS keywords.
Generic metrics make geodesic nets dense.
problem Density of geodesic nets under generic metrics.
method Proving density for Baire-generic metrics.
result Union of geodesic nets images is dense.
The paper introduces new estimators for multivariate functions using Fourier methods.
problem Estimating multivariate functions like densities and regression functions.
method Monte Carlo estimators based on the Fourier integral theorem.
result Established rates of convergence for new estimators, often superior to existing methods.