dtSNE preserves local densities in low-dimensional embeddings.
problem Local density differences are not accurately preserved in tSNE and UMAP.
method dtSNE, which approximately conserves local densities.
result dtSNE provides more accurate local density depictions.
Efficiently sparsifies simplicial complexes using local densities of states.
problem Prohibitive computational requirements for dense simplicial complexes.
method Probabilistic sparsification using local densities of states and kernel-ignoring decomposition.
result Approximates the spectrum of the original SC with a sparser surrogate SC.
This paper presents a simple but effective density-based outlier detection approach with the local kernel density estimation (KDE). A Relative Density-based Outlier Score (RDOS) is introduced to measure the local outlierness of objects, in which the density distribution at the location of an object is estimated with a …
New approach improves computational efficiency of Bass Local Volatility model.
problem Eliminate interpolation and improve computational efficiency in local volatility models.
method Combines local quadratic estimation and lognormal mixture tails for state price densities; uses trapezoidal rule for numerical convolutions.
result Proposed method outperforms traditional numerical methods in option pricing and market case studies.
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps define better justified sampling algorithms for deep learning based on auto-encoder v…
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.
Single-molecule localization fluorescence microscopy constructs super-resolution images by sequential imaging and computational localization of sparsely activated fluorophores. Accurate and efficient fluorophore localization algorithms are key to the success of this computational microscopy method. We present a novel l…
A new pricing controller handles resource constraints to infer target prices effectively.
problem Resource constraints prevent fixed-price inference, leading to support exclusion.
method Formalizes support-exclusion failure, designs a target-aware controller, and uses a realized information clock.
result The controller can certify feasible target bands and log continuous local densities, leading to polynomial rates of inference.
The paper defines and studies discrete p-density and compression-radius profiles of lattice knots.
problem Understanding geometric properties of lattice knots.
method Develops a framework for discrete p-density and compression-radius profiles of lattice knots, studying them on length-filtered sets and finite move-graph exploration.
result Density and compression-radius values are not monotone, illustrating distinct optimization problems.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and surfaces. However, the problem of unwrapping or unfolding manifolds has received r…
Crowd counting problem aims to count the number of objects within an image or a frame in the videos and is usually solved by estimating the density map generated from the object location annotations. The values in the density map, by nature, take two possible states: zero indicating no object around, a non-zero value i…
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
Conformal-DP improves differential privacy on manifold data by calibrating perturbations based on local densities.
problem Lack of density-awareness in existing differential privacy mechanisms for manifold data leads to biased and suboptimal privacy-utility trade-offs.
method Proposes Conformal-DP, a density-aware differential privacy mechanism using conformal transformations to calibrate perturbations based on local densities.
result Demonstrates improved privacy-utility trade-off in heterogeneous data distribution settings compared to state-of-the-art mechanisms.
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…
Develops a local Fokker--Planck geometric framework for more accurate score estimation.
problem Inaccurate estimation of score function in non-linear, state-dependent drifts.
method Local Fokker--Planck geometric framework, time change to cumulative-variance coordinate, heat-ball mean-value representations, exact high-dimensional sampling.
result Exact local mean-value representations for the score and density, improved accuracy in low-density regions.
Proposes a method combining CNFs and rejection-resampling for sampling from unnormalized densities.
problem Sampling from unnormalized probability densities, especially multimodal ones.
method Combines continuous normalizing flows with rejection-resampling steps based on importance weights.
result The method improves sampling accuracy and performance compared to state-of-the-art methods.
Machine learning predicts electronic density of states for condensed matter.
problem Predicting the electronic density of states (DOS) in complex condensed matter systems.
method Developed a machine learning framework to predict DOS from density functional theory data, considering geometric configurations of atoms.
result Demonstrated the model's effectiveness in predicting DOS and its components for various silicon configurations.
G-GLN extends GLNs to multiple regression and density modeling.
problem Learning features in deep neural networks.
method G-GLN uses a distributed and local credit assignment mechanism based on optimizing a convex objective.
result G-GLN achieves competitive or state-of-the-art performance on regression benchmarks.
EagleEye detects localized density anomalies in multivariate data.
problem Identifying signal events, regime changes, or model mismatch in scientific data.
method EagleEye pinpoints local over- and under-densities by assigning anomaly scores based on binary membership sequences and binomial null models.
result EagleEye can detect genuine local anomalies and estimate background purity.
A new clustering algorithm reduces density peaks clustering's computational complexity.
problem High computational complexity of density peaks clustering.
method Sparse distance matrix, sparse search, K-d tree, second-order difference method.
result Reduced computational complexity from O(n2K) to O(n(n1−1/K+k)). In this work, we develop a new approach to generative density estimation for exchangeable, non-i.i.d. data. The proposed framework, FlowScan, combines invertible flow transformations with a sorted scan to flexibly model the data while preserving exchangeability. Unlike most existing methods, FlowScan exploits the intra…
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonpa…
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
Improved manifold-adaptive dimension estimator for better data complexity assessment.
problem Estimating intrinsic dimensionality of complex data.
method Revised and improved Farahmand-Szepesvári-Audibert (FSA) estimator, incorporating probability density function and median.
result Median-FSA estimator outperforms existing methods in accuracy and robustness.
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the…
Recently, deep clustering, which is able to perform feature learning that favors clustering tasks via deep neural networks, has achieved remarkable performance in image clustering applications. However, the existing deep clustering algorithms generally need the number of clusters in advance, which is usually unknown in…
Efficient clustering in high dimensions with Quick Shift and LSH.
problem Density-based clustering in high-dimensional data.
method Combines Quick Shift and LSH for efficient density estimation.
result Achieves almost linear time complexity for consistency.
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…
We forecast S&P 500 excess returns using a flexible Bayesian econometric state space model with non-Gaussian features at several levels. More precisely, we control for overparameterization via novel global-local shrinkage priors on the state innovation variances as well as the time-invariant part of the state space mod…
MFRDE uses medians of forest estimators to robustly estimate densities in noisy data.
problem Robust density estimation in the presence of outliers.
method MFRDE uses pointwise median operation on forest density estimators fitted on subsampled datasets.
result MFRDE achieves robustness against all outliers while maintaining accuracy for density estimation.
LAAT detects multiple low-density manifolds in noisy data.
problem Detecting multiple low-density manifolds in noisy data.
method Locally Aligned Ant Technique (LAAT) based on Ant Colony Optimization.
result LAAT recovers multiple manifolds in extremely noisy data.
EMDE efficiently estimates manifold densities for diverse recommendation systems.
problem Efficiently estimating manifold densities for multi-modal recommendation systems.
method EMDE (Efficient Manifold Density Estimator) framework for arbitrary vector representations.
result Established new state-of-the-art results in top-k and session-based recommendation settings.
A novel method computes Wigner kernels for atomic environments, achieving state-of-the-art accuracy.
problem Efficiently describing local atomic environments in materials science.
method Computes fully equivariant and body-ordered kernels iteratively, independent of basis.
result Achieves state-of-the-art accuracy on the QM9 benchmark dataset.
Local index density of perturbed de Rham complex is invariant under certain conditions.
problem Invariance of local index density for perturbed de Rham complex.
method Invariance theory applied to perturbed Laplacian and local index density.
result Local index density is invariant under perturbation by closed 1-forms.
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.
Paper proposes a new method for conditional coverage in conformal prediction.
problem Lack of strong conditional coverage guarantees in existing conformal prediction methods.
method Modified non-conformity score using local approximation of conditional distribution.
result Unified framework and empirical evaluations show advantage of the new method.
DoSE improves OOD detection by estimating model probability density.
problem Poor specificity of model likelihoods for OOD detection.
method DoSE uses density of states concept to avoid direct model probability comparison.
result DoSE achieves state-of-the-art performance on OOD detection benchmarks.
Optimal testing for densities under local differential privacy constraints.
problem Testing goodness-of-fit for densities under privacy constraints.
method Estimation of quadratic distance and minimax separation rates.
result First minimax optimal test under local differential privacy constraints.
A new clustering algorithm GDT improves on HDBSCAN for uneven data.
problem Data clustering with uneven distribution and high noise.
method GDT combines local and global structures, forming local clusters and estimating a global topological graph based on connectivity between clusters.
result GDT achieves SOTA performance on various datasets with low time complexity.
We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the parti…
Novel flows generate molecules without post-processing.
problem Generating new molecules efficiently and without post-processing issues.
method Continuous normalizing E(3)-equivariant flows based on node ODEs coupled as a graph PDE.
result Generated samples achieve state-of-the-art performance on QM9 and ZINC250K benchmarks.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.
Efron et al. (2001) proposed empirical Bayes formulation of the frequentist Benjamini and Hochbergs False Discovery Rate method (Benjamini and Hochberg,1995). This article attempts to unify the `two cultures' using concepts of comparison density and distribution function. We have also shown how almost all of the existi…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based state estimation models currently used for data filtering, prediction and anoma…
Neural net reconstructs dark matter density from halo velocities.
problem Reconstructing local dark matter density from halo velocities.
method Hybrid architecture combining U-Net and DeepSets.
result Hybrid network recovers density amplitudes and phases better than U-Net.
Paper proposes a robust LPR method using similarity kernels.
problem Outliers and high-leverage points affect traditional LPR's accuracy.
method Integrates predictor and response variables in weighting mechanism using a conditional density kernel.
result Lower empirical bias compared to iterative robust LOWESS.