Develops local curvature estimates for mean curvature flow.
problem Sharp curvature pinching estimates for mean curvature flow.
method Local version of Huisken-Stampacchia iteration.
result Local curvature estimates do not depend on noncollapsing quality.
Estimates Kähler metrics with noncollapsing volume under complex Monge-Ampère constraints.
problem Volume noncollapsing for Kähler metrics induced by complex Monge-Ampère equations.
method Proves local volume noncollapsing estimate with Ricci curvature lower bound.
result Establishes diameter and gradient estimates for Kähler metrics.
Global and local estimates for a curvature equation on manifolds with boundary.
problem Estimating modified σ2 curvature equation with boundary conditions. method Global and local C2-estimates established. result Global C2-estimates for the modified σ2 curvature equation. Estimates manifold dimension using local graph structure.
problem Estimating the intrinsic dimension of manifolds from data.
method Regression on local PCA coordinates, focusing on local graph structure.
result Proposed QE and TLS estimators outperform existing methods.
New GP model estimates piecewise continuous functions.
problem Piecewise continuous regression functions in scientific and engineering applications.
method Local Gaussian process model with partitioned local data and joint estimation of boundaries.
result Superior performance over conventional GP models in estimating piecewise regression functions.
New estimator robust to adversarial noise and data heterogeneity.
problem Sensitive to adversarial noise and poor performance with heterogeneous data.
method Distributionally robust estimator minimizing worst-case conditional expected loss over adversarial distributions.
result Efficiently finds non-parametric local estimates via convex optimization.
Proves local noncollapsing estimate for mean curvature flow.
problem Ensuring noncollapsing in mean curvature flow.
method Combining local estimate with earlier work on ancient solutions.
result Ancient convex solutions that sweep out entire space are noncollapsed.
We study a basic private estimation problem: each of n users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential privacy for each user. Informally, local differential privacy requires that each data …
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamenta…
Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.
This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.
problem Estimating chaotic dynamics and parameters from observations.
method Local ensemble Kalman filters with covariance and local domain localisation.
result Rigorously updating global parameters using a local domain ensemble Kalman filter.
The study sharpens local Bernstein estimates for Laplace eigenfunctions on compact manifolds.
problem Understanding local growth properties of Laplace eigenfunctions on compact Riemannian manifolds.
method Refined Donnelly-Fefferman method based on L2--Carleman estimates, combined with elliptic regularity and patching of local Carleman estimates. result Almost sharp local Lp--Bernstein inequalities for p∈[1,∞]. Proposes a new regression method using Lp-norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial Lp-norm regression, replacing weighted least squares with weighted Lp-norm estimation. result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
Localizes curvature estimates for evolving hypersurfaces under various flows.
problem Establishing curvature estimates for evolving hypersurfaces under different flow conditions.
method Adapted localization of Huisken--Stampacchia iteration method to fully nonlinear flows.
result Asymptotically sharp curvature pinching estimates for general flows.
Improved locally private sparse estimation with multiple samples per user.
problem Challenges in high-dimensional locally private sparse estimation.
method Proposes a framework for user-level locally private sparse linear regression with multiple samples per user.
result Eliminates the dependency of dimensionality on error bounds, achieving tighter error bounds.
We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network uses a convex optimization based algorithm that provides a locally optimum soluti…
We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the L2 Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from C0 estimates. Also, the method is flexible and can be applied to a large class of equations.
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
New estimator adapts to various error distributions.
problem Adapting to different error distributions in nonparametric regression.
method Introduces outrigger local polynomial estimator with modified weighted least squares.
result Minimax optimal over Hölder classes with multiplicative factor.
Curvature estimate for stable free boundary minimal hypersurfaces in wedge-shaped manifolds.
problem Estimating curvature of stable free boundary minimal hypersurfaces in wedge-shaped manifolds.
method Compactness theorem and Schoen-Simon-Yau estimates.
result Curvature estimate for free boundary minimal hypersurfaces in wedge-shaped manifolds.
A new algorithm estimates mean under varying user data sizes with local differential privacy.
problem Mean estimation with user-level local differential privacy under varying data sizes.
method Distribution-aware mean estimation algorithm for users with varying data sizes.
result Upper and lower bounds on the worst-case risk for mean estimation are derived.
Study local curvature estimates and existence of conformal metrics on noncompact manifolds.
problem Deriving local C0-estimates and existence of conformal metrics with prescribed curvature. method Utilizing Aviles-McOwen's result and its nonlinear extension, combined with asymptotic conditions.
result Proved existence of complete conformal metrics with prescribed curvature functions.
Extends ESGVI for UWB localization with skewed noise, improving state estimation accuracy.
problem Improving state estimation accuracy in UWB localization with skewed noise.
method Generalizes ESGVI to matrix Lie groups and introduces non-Gaussian factors.
result Improved accuracy in UWB localization with NLOS and multipath effects.
Bagging reduces variance in LID estimation by preserving local distribution of NN distances.
problem High estimation variance from limited data in small neighborhoods.
method Subbagging to preserve local distribution of NN distances, combined with ensemble size.
result Bagging significantly reduces variance and MSE in LID estimation.
Identifying the location of a disturbance and its magnitude is an important component for stable operation of power systems. We study the problem of localizing and estimating a disturbance in the interconnected power system. We take a model-free approach to this problem by using frequency data from generators. Specific…
Estimates LLC for deep linear networks up to 100M parameters.
problem Quantifying model complexity for large-scale deep learning architectures.
method Empirical estimation of LLC using a method developed for DLNs.
result LLC can be accurately measured for DLNs up to 100M parameters.
Paper proves curvature estimates for a specific flow on Kähler manifolds.
problem Proving local curvature estimates for a specific flow on Kähler manifolds.
method Proves local curvature estimates for the κ-LYZ flow over Kähler manifolds. result Generalizes the long time existence of the flow.
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.
In this short note we present local derivative estimates for heat equations on Riemannian manifolds following the line of W.-X. Shi. As an application we generalize a second derivative estimate of R. Hamilton for heat equations on compact manifolds to noncompact case.
LIDL estimates local intrinsic dimension in high dimensions.
problem Estimating local intrinsic dimension in high-dimensional data.
method Approximate likelihood using parametric neural density estimation.
result LIDL scales to thousands of dimensions and yields competitive results.
This paper analyzes Local SGD for federated learning, achieving both statistical and communication efficiency.
problem Statistical estimation and inference in federated learning with decentralized data.
method Local SGD, a multi-round estimation procedure using intermittent communication.
result Local SGD achieves both statistical efficiency and communication efficiency.
DNNs improve localization from channel estimates, overcoming practical impairments.
problem Improving localization accuracy from channel estimates in Massive MIMO systems.
method Principled feature design for DNNs invariant to practical impairments.
result DNN achieves high localization accuracy and generalization capability.
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.
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
Paper proposes methods to localize sources in WSNs without knowing sensor parameters.
problem Source localization in WSNs without sensor parameter knowledge.
method Hitting set approach and feature selection method.
result Effective source localization methods validated through simulations.
Establishes refined singularity estimate for nonnegative n-superharmonic functions in locally conformally flat manifolds.
problem Analyzing volume growth and verifying Cohn-Vossen inequality in locally conformally flat manifolds.
method Refined singularity estimate and characterization of volume growth.
result Analytically characterizes volume growth and verifies Cohn-Vossen inequality.
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…
A new method selects covariates for causal effect estimation without strong assumptions.
problem Estimating causal effects without global causal structure learning and strong assumptions.
method Local covariate selection method that avoids pretreatment and causal sufficiency assumptions.
result The method achieves accurate causal effect estimation with improved computational efficiency.
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 …
In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to …
The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.
Paper optimizes privacy-preserving distribution estimation for sparse data.
problem Sparse distribution estimation under local differential privacy constraints.
method Compressive sensing approaches for privacy-preserving estimation.
result Significant reduction in sample complexity for approximately sparse distributions.
Locally private mechanisms' output divergence bounds derived.
problem Bounding divergence between locally private mechanisms' outputs.
method Sharp upper bounds on divergence between input and output distributions.
result Established locally private versions of estimation risk bounds.
Uniform volume estimate for Kähler metrics in big cohomology classes.
problem Estimating volume for singular Kähler metrics in big cohomology classes.
method Generalized mixed energy estimate for functions in complex Sobolev space to big cohomology classes.
result Uniform non-collapsing volume estimate for local Kähler metrics.