Study on volume and determinant densities of hyperbolic rational links.
problem Properties and distributions of volume and determinant densities of hyperbolic rational links.
method Construction of sequences of alternating knots and analysis of density distributions.
result Volume and determinant densities of hyperbolic rational links converge to any value in the interval [0,v_{oct}].
Study exact minimax rates for density estimation over convex classes, extending previous work.
problem Deriving minimax rates for density estimation over convex density classes.
method Building on Le Cam's work, determine exact minimax rates using local metric entropy.
result Exact minimax rates derived for any convex density class, including nonparametric and parametric cases.
DADC algorithm improves clustering for data with varying density.
problem Sparse cluster loss and cluster fragmentation in density peak clustering.
method Domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble.
result DADC achieves more reasonable clustering results on data with varying density.
Study finds a linear lower bound on conformal dimension for random hyperbolic groups.
problem Understanding conformal dimension in random hyperbolic groups.
method Building undistorted round trees from lower density groups.
result Achieves a linear lower bound in l at all densities 0<d<1/2. Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
Proposes a new hierarchical clustering method combining DP and DBSCAN strengths.
problem Combining strengths of DP and DBSCAN for arbitrary shape clusters.
method DC-HDP: Combines Density Peak and Density-Connectivity approaches.
result Produces best clustering results on 14 datasets.
Defines hierarchical clustering axioms for various densities.
problem Defining hierarchical clustering for different types of densities.
method An axiomatic approach to piecewise constant densities, then extending to general densities.
result Our axiomatic definition results in Hartigan's cluster tree under certain conditions.
Quantum computers outperform classical methods in density modeling.
problem Density modeling with quantum computers.
method Quantum-classical separation for density modeling.
result Quantum computers offer a super-polynomial advantage over classical algorithms for density modeling.
We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertical fibers minimize vertical surface area among regions bounding the same volume and use these results to conclude that in many such…
New density estimator from Markov Chains outperforms KDE.
problem Density estimation from Markov Chains.
method Nonparametric density estimator based on Markov Chains.
result Consistent and outperforms KDE in large sample size and high dimensionality.
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…
New binary loss functions improve density ratio estimation accuracy.
problem Improving accuracy of density ratio estimators using binary classifiers.
method Characterized loss functions based on prescribed error measures in Bregman divergences.
result Novel loss functions prioritize accurate estimation of large density ratio values.
Quantum method improves neural density estimation in high dimensions.
problem High-dimensional density estimation with poor performance and high computational complexity.
method Adaptive Fourier features based on quantum density matrices, integrated with neural networks.
result Competitive performance compared to state-of-the-art methods in various datasets.
Paper develops estimators for unbounded density ratios with applications in error control.
problem Estimating density ratios with unbounded domains and ranges.
method Least squares and logistic regression loss functions for density ratio estimation.
result Established upper bounds on estimation errors with optimal rates for unbounded density ratios.
Paper introduces MoM-KDE for robust density estimation robust to anomalous data.
problem Density estimation robustness to anomalous data.
method Combines Kernel Density Estimation and Median-of-Means principle.
result Achieves competitive results with lower computational complexity compared to other robust estimators.
Study on stable Hamiltonian topology finds non-density of certain structures.
problem Non-density of stable hypersurfaces and Hamiltonian structures.
method Proving non-density results for stable hypersurfaces and Hamiltonian structures in various dimensions.
result Non-density of stable hypersurfaces and Hamiltonian structures in specific isotopy and homotopy classes.
We link probability density functions to Fisher information metrics.
problem Constructing probability density functions from Fisher information metrics.
method Utilizing the spatially disjoint product of probability density functions and their Fisher information metric tensors.
result A method for constructing arbitrary Riemannian Fisher information metric tensors.
The paper proposes a method to create density-equalizing maps for open surfaces.
problem Creating flattening maps of simply-connected open surfaces with prescribed density distributions.
method Density diffusion principle and algorithm for computing flattening maps.
result Area-preserving parameterizations of simply-connected open surfaces can be easily computed.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
New model for density estimation using tensor trains.
problem Estimation of high-dimensional probability density functions.
method Tensor train-based density estimation (TTDE) with Riemannian optimization.
result TTDE outperforms competitors in training speed and performance.
Estimates copula density for complex data distributions.
problem Estimating copula density from observed data.
method Neural network-based copula density neural estimation (CODINE).
result Novel approach capable of modeling complex distributions.
Combines coarse learners for nonparametric probabilistic regression.
problem Predicting full probability density functions without strong assumptions.
method Combining gradient boosted forests trained on coarsened target values.
result Prediction intervals have high fidelity and provide valuable insights.
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density…
Paper improves speech separation by using deep neural networks for more accurate density priors.
problem Improving the accuracy of source priors for independent vector analysis in speech separation.
method Estimating the derivative of speech density using deep neural networks to optimize performance indices.
result Neural network density priors outperform previous ones in convergence speed and SIR.
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.
Cubic-Spline Flows improve autoregressive flow performance in density estimation.
problem Improving the performance of flow-based models in density estimation.
method Stacking a new coupling transform based on monotonic cubic splines with LU-decomposed linear layers.
result Cubic-Spline Flows close the gap with autoregressive flows on density-estimation tasks.
Study on flow-based methods for capturing tail properties in densities.
problem Flow-based methods struggle with capturing non-Gaussian tails.
method Characterize and adapt triangular maps to capture tail properties.
result Flow models lack the ability to capture non-Gaussian tails.
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.
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting density forecasts will inevitably be downgraded by model mis-specification. In o…
Density destructors simplify complex PDFs to maximize entropy, linking to information theory.
problem Complex multivariate PDFs are hard to analyze.
method Invertible transforms that progressively remove structure from PDFs.
result Density destructors can improve estimates of information theoretic quantities.
Study kernel density estimation for dynamical systems with unique invariant density.
problem Density estimation for dependent observations from dynamical systems.
method Employing C-mixing to measure dependence, universal consistency and convergence rates are established. result Kernel density estimator is universally consistent and achieves convergence rates under L1-norm and L∞-norm. Transforms conditional density estimation into a nonparametric regression problem.
problem Conditional density estimation in high dimensions.
method Introduces auxiliary samples to transform into nonparametric regression.
result Estimator converges to true conditional density in data limit.
Proposes SD-KDE for density estimation using debiased kernel density with score-based adjustments.
problem Density estimation with bias in kernel density estimation.
method Adjusts data points by taking a step along the estimated score function, then applies standard KDE with modified bandwidth.
result Significantly reduces mean integrated squared error compared to standard Silverman KDE, especially with noisy score function estimates.
Boosted density estimation improves convergence guarantees without unrealistic assumptions.
problem Lack of formal convergence guarantees in density estimation methods.
method Introducing a weak learning assumption from boosting, we develop an iterative boosted density estimation algorithm.
result Formal convergence results with rates for density estimation without heavy assumptions.
CDF transform-and-shift homogenizes cluster densities for better clustering.
problem Inhomogeneous cluster densities bias algorithms towards dense clusters.
method Apply a Cumulative Distribution Function (CDF) transform-and-shift method to homogenize cluster densities.
result The method outperforms existing solutions in clustering and anomaly detection.
Researchers classify invariant operators on weighted densities.
problem Classifying invariant differential operators on weighted densities.
method Investigated the aff(n∣1)-module structure and invariant binary differential operators. result Computed the first aff(n∣1)−relative differential cohomology. Optimal approximation factor of 2 achieved in density estimation.
problem Finding the closest density to an unknown target density in terms of total variation.
method Developed adaptive and static approaches based on geometric and surrogate metrics to achieve the optimal approximation factor of 2.
result Achieved an optimal approximation factor of 2 for density estimation.
New method learns models from data density and generates samples.
problem Learning models that estimate data density and generate samples.
method Denoising density estimators (DDEs) trained to minimize KL-divergence.
result Our method converges to correct solution without specific network architecture.
Sum-of-Squares flow improves autoregressive and flow-based density estimation.
problem Density estimation in high dimensions with limitations of existing methods.
method Proposes a Sum-of-Squares (SOS) flow framework based on triangular maps.
result SOS flow achieves competitive results in simulations and real-world datasets.
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
Paper tackles unbounded density ratio estimation for covariate shift adaptation.
problem Understudied challenge in statistical learning: unbounded density ratios.
method Three-step estimation method: relative density ratio, truncation, and transformation.
result Established rigorous convergence guarantees for density ratio and regression estimators.
Paper tackles privacy-preserving data density issues using deconvolution.
problem Privacy-preserving noise affects data density, leading to under/over-estimation.
method Develops deconvoluting kernel density estimators and regression models.
result Demonstrates improved accuracy in estimating heavy-hitters with locally differential data.
Mean shift clustering finds the modes of the data probability density by identifying the zero points of the density gradient. Since it does not require to fix the number of clusters in advance, the mean shift has been a popular clustering algorithm in various application fields. A typical implementation of the mean shi…
This paper studies sparse density estimation via ℓ1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities an…
The paper solves the isoperimetric problem with perimeter density \(|x|^p\).
problem Isoperimetric problem with perimeter density \(|x|^p\).
method Analyzes the problem in \(n=2\) and \(n\geq 3\) dimensions, characterizing cases and showing non-generalization.
result Characterizes the isoperimetric problem for \(0 \leq p \leq 1\) and \(-\infty < p < -1\) in \(n=2\). Shows results do not generalize for \(-n+1 < p < 0\) in \(n \geq 3\).
Paper develops a method for estimating spectral density matrices in high-dimensional time series.
problem Estimating spectral density matrices in high-dimensional time series.
method Thresholded versions of averaged periodograms for regularized estimation.
result Consistent estimation of spectral density matrices possible under high-dimensional regime.
The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.
problem Classifying non-harmonic biharmonic quadratic forms between spheres.
method Proving non-harmonic biharmonic quadratic forms have constant energy density and classifying them.
result Non-harmonic biharmonic quadratic forms have constant energy density (m+1)/2.