Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
Holomorphic cylinders converge to disks joined by flow lines.
problem Convergence of perturbed holomorphic cylinders.
method Exponential estimates and flow line computation.
result Holomorphic cylinders converge to two disks joined by a flow line.
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
Improved convergence and curvature estimate for parabolic Allen-Cahn equation.
problem Mean curvature flow and its parabolic analogue.
method Improved convergence property and curvature estimate.
result Curvature estimate for parabolic Allen-Cahn equation.
Uniform estimates prove convergence of Chern-Ricci flow on complex surfaces.
problem Proving convergence of Chern-Ricci flow on complex minimal surfaces.
method Uniform diameter estimates, volume non-collapsing estimates, Gromov-Hausdorff convergence; surface torsion estimate, uniform total variation bound, Green-weighted L^2 estimate, linear iteration of real Poisson equations.
result Uniform diameter estimates, volume non-collapsing estimates, Gromov-Hausdorff convergence for normalized Chern-Ricci flow on complex minimal surfaces.
New method shows Hessian estimator from random samples converges to true Hessian on complex manifolds.
problem Uncertainty in Hessian estimator accuracy on complex manifolds with boundaries and nonuniform sampling.
method Locally fitting quadratic polynomials, rigorous theoretical analysis under mild conditions.
result The Hessian estimator asymptotically converges to the true Hessian, even near boundaries.
The paper develops a uniform function estimator in RKHS for regression.
problem Reconstructing functions from noisy data at random locations.
method Using reproducing kernel Hilbert spaces and Gaussian random fields.
result The estimator converges uniformly to the conditional expectation.
The paper analyzes rates of convergence for optimal transport map estimators using barycentric projections.
problem Estimating optimal transport maps from data sampled according to two distributions.
method Comprehensive analysis of rates of convergence for plug-in estimators defined via barycentric projections.
result New stability estimate for barycentric projections under minimal smoothness assumptions.
Study provides convergence rates for risk measure estimation.
problem Estimating risk measures from limited data.
method Plug-in estimation using empirical measures.
result Non-asymptotic convergence rates for risk measure estimation.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
problem Estimating the probability of default (PD) using limited historical data.
method Adopted the Merton model and analyzed phase transitions in default correlation.
result PD estimation converges slowly when temporal correlation decays by power law less than one.
Estimates the rate of convergence of mean curvature flow solutions.
problem Understanding the convergence rate of mean curvature flow solutions.
method Estimates the upper bound of convergence rate to a limit self-similar solution.
result Solutions converging faster than any fixed exponential rate must be shrinkers themselves.
In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, t…
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 proof shows faster convergence rate for robust estimation with Lasso in adversarially contaminated outputs.
problem Robust estimation of parameters in the presence of adversarial output contamination.
method Extended Lasso with Huber loss function and L 1 L_1 L 1 penalty, focusing on specific properties of the Huber function. result Same convergence rate as Dalalyan and Thompson (2019), but with a different proof.
Machine learning improves high-dimensional matrix estimation.
problem Efficient estimation of high-dimensional matrices.
method Integrates machine learning with classical optimization algorithms for high-dimensional matrix estimation.
result The reparameterized LADMM achieves faster convergence and higher accuracy.
New method estimates convergence bounds for nonlinear Markov chains.
problem Difficulty in describing properties of nonlinear Markov chains.
method Coupling Markov chains to reconstitute distribution relationships and estimate convergence bounds.
result Estimation of convergence bounds is more precise than existing results.
Paper analyzes faster convergence rates for reinforcement learning from offline data.
problem Analyzing faster convergence rates for reinforcement learning from offline data.
method Fine analysis of reinforcement learning from offline data, providing fast rates for regret convergence.
result The paper provides fast rates for the regret convergence, showing that the level of exponentiation depends on the noise in the decision-making problem.
The paper improves OT map estimation rates without strict assumptions.
problem Estimating optimal transport maps under practical conditions.
method Developed new convergence rates and scalable algorithms.
result Improved convergence rates for OT map estimation without restrictive assumptions.
Paper establishes convergence rates for learning elliptic pseudo-differential operators.
problem Learning elliptic pseudo-differential operators in partial differential equations.
method Wavelet-Galerkin framework, structured infinite-dimensional regression problem, sparse estimator, matrix compression, nested-support strategy.
result Obtained convergence rates for the estimator and efficient Galerkin solver.
Paper develops RGN method for estimating low-rank tensors from noisy measurements.
problem Estimating low-rank tensors from noisy linear measurements.
method Riemannian Gauss-Newton (RGN) method for efficient low-rank tensor estimation.
result First local quadratic convergence guarantee of RGN for low-rank tensor estimation in noisy settings.
Study Fourier estimator for spot volatility with unbounded coefficients and jumps.
problem Estimating spot volatility with unbounded coefficients and jumps in price process.
method Fourier estimator for spot volatility, convergence analysis for unbounded coefficients and jumps.
result Convergence of trigonometric polynomial to volatility's path, almost sure convergence of reconstructed volatility.
Paper derives convergence rates for NPMLE in Hellinger distance using deep neural networks.
problem Difficulty in proving convergence of excess risk in nonparametric logistic regression.
method Unified approach for analyzing NPMLE, deriving convergence rates in Hellinger distance.
result Derives nearly optimal convergence rates for NPMLE with deep neural networks.
The study provides guarantees for diffusion-based models under log-concave data, offering best-known convergence rates.
problem Theoretical guarantees for convergence of diffusion-based generative models under log-concave data distributions.
method Assumption of strongly log-concave data distributions, Lipschitz continuous functions for score estimation, and novel auxiliary process.
result Best known upper bounds for Wasserstein-2 distance between Gaussian distribution and sampling algorithm.
Unified view of score estimators for flexible densities.
problem Estimating the score from unknown distributions.
method Regularized nonparametric regression framework.
result Unified convergence analysis and new estimators with desirable properties.
A study on α \alpha α -GANs proving convergence and estimation guarantees.
problem Analyzing the convergence and estimation guarantees of α \alpha α -GANs. method Proved a correspondence between α \alpha α -GANs and f f f -divergences, and provided estimation bounds. result Estimation bounds indicate diverse GAN behavior as a function of α \alpha α . The study finds counterexamples to curvature estimates for minimizing surfaces.
problem Curvature estimates for minimizing surfaces in metric convergence.
method Constructing sequences of smooth minimizing surfaces in metrics converging to Euclidean.
result Found counterexamples with diverging L 2 L^2 L 2 norm of second fundamental form. This paper analyzes and guarantees convergence of prior-guided ZO algorithms.
problem Understanding convergence properties of prior-guided zeroth-order optimization algorithms.
method Analysis of convergence under a greedy descent framework with various gradient estimators, and development of ARS algorithm.
result Convergence guarantee for prior-guided random gradient-free (PRGF) algorithms and accelerated random search (ARS) algorithm.
The paper analyzes the risk of CV-tuned regularized estimators and connects it to SURE.
problem Understanding the risk of CV-tuned regularized estimators.
method Derives asymptotic risk function of CV-tuned estimators and connects it to SURE.
result The risk function provides a more detailed picture of predictive performance than uniform bounds.
We consider the problem of estimating the curvature profile along the boundaries of digital objects in segmented black-and-white images. We start with the curvature estimator proposed by Roussillon et al., which is based on the calculation of \emph{maximal digital circular arcs} (MDCA). We extend this estimator to the …
Study on how sampling works for complex data functions.
problem Analyzing convergence of sampling algorithms for RKHS functions.
method Minimalistic assumptions on kernel and data, error estimates in RKHS norm, uniform convergence on compact domains.
result New convergence rates for Lipschitz and Hölder continuous kernels.
Study analyzes convergence of parameter estimation in contaminated mixture of experts.
problem Challenges in learning from prompts in large-scale models.
method Convergence analysis, distinguishability condition, partial differential equations.
result Comprehensive convergence rates and minimax lower bounds for parameter estimation.
The paper strengthens the classical result of MLE convergence to a Gaussian distribution.
problem The classical result of MLE convergence to a Gaussian distribution.
method Sub-Gaussian concentration and entropic normality of the normalized MLE.
result Entropic central limit theorem for a smoothed version of the estimator.
Paper develops an online learning algorithm for functional data models.
problem Recovering slope functions or predictors in functional data models.
method Online regularized learning algorithm in reproducing kernel Hilbert spaces with polynomially decaying step-size.
result Established fast convergence rates for estimation error without capacity assumption.
Crowdsourcing has become a primary means for label collection in many real-world machine learning applications. A classical method for inferring the true labels from the noisy labels provided by crowdsourcing workers is Dawid-Skene estimator. In this paper, we prove convergence rates of a projected EM algorithm for the…
Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.
problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.
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.
In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order 1 / 2 1/2 1/2 . This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…
New analysis of SGD with MCMC gradient estimator shows convergence rate and saddle point escape.
problem Analyzing SGD with MCMC gradient estimator under complex conditions.
method Introduced MCMC-SGD, analyzed convergence rate and saddle point escape using Bernstein inequality.
result Proven first order convergence rate O ( log K / n K ) O(\log K/\sqrt{n K}) O ( log K / n K ) and saddle point escape at least O ( ε − 11 / 2 log 2 ( 1 / ε ) ) O(ε^{-11/2}\log^{2}(1/ε) ) O ( ε − 11/2 log 2 ( 1/ ε )) steps. Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
Study geodesic Lie groups' convergence to limits with quantitative estimates.
problem Quantifying convergence rates of geodesic Lie groups to their limits.
method Estimates on the difference between original metrics and asymptotic/tangent metrics.
result Sharpens existing bounds on convergence rates.
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In particular, even for those estimators whose MSE convergence rates are known, the asympt…
FlexCodeTS is a flexible time series density estimator.
problem Estimating conditional densities for time series data.
method Nonparametric conditional density estimator based on arbitrary regression methods.
result FlexCodeTS adapts its convergence rate based on the chosen regression method.
BBVI with STL converges geometrically under perfect specification, with quadratic variance bound.
problem Convergence rate of BBVI with STL estimator.
method Proved geometric convergence rate with quadratic variance bound for BBVI with STL estimator.
result BBVI with STL converges geometrically under perfect variational family specification.
Study continuity equation on Hopf and Inoue surfaces, proving estimates and convergence.
problem Analyzing the continuity equation on specific complex surfaces.
method Extended La Nave-Tian's continuity equation to Hermitian setting, proving estimates and Gromov-Hausdorff convergence.
result Proved a priori estimates for solutions on Hopf and Inoue surfaces, and convergence of Inoue surfaces to a circle.
Paper proposes a new estimator for nested expectations with faster convergence.
problem Estimating nested expectations is computationally challenging.
method Nested kernel quadrature estimators with proof of faster convergence rate.
result The proposed method requires fewer samples for accurate estimation.
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. W…
Improved GANs estimate convergence rate for density estimation.
problem Improving the accuracy of density estimation with GANs.
method Proved an oracle inequality for JS divergence between GAN estimate and true density.
result JS-divergence rate of convergence is ( log n / n ) 2 β / ( 2 β + d ) (\log{n}/n)^{2β/(2β+ d)} ( log n / n ) 2 β / ( 2 β + d ) . In this paper we develop an Expectation Maximization(EM) algorithm to estimate the parameter of a Yule-Simon distribution. The Yule-Simon distribution exhibits the "rich get richer" effect whereby an 80-20 type of rule tends to dominate. These distributions are ubiquitous in industrial settings. The EM algorithm presen…