Optimally estimate distances on surfaces using reconstructed meshes.
problem Estimating intrinsic distances on smooth submanifolds.
method Reconstruction of the surface using a tangential Delaunay complex, and Isomap variant.
result Minimax optimality achieved for distance estimation.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ γ γ -smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Paper analyzes kNN estimator for KL divergence, proving its optimality.
problem Estimating KL divergence from identical samples.
method kNN estimator based on nearest neighbor distances.
result kNN method is asymptotically rate optimal for KL divergence estimation.
We study the minimax optimal rate for estimating the Wasserstein- 1 1 1 metric between two unknown probability measures based on n n n i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures u…
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
Kernel estimator optimally recovers function from noisy exponential Radon transform.
problem Inverting noisy exponential Radon transform of a function.
method Proposed a kernel estimator to estimate the true function.
result The estimator converges to the true function at minimax optimal rate.
Study confirms optimal minimax rate for nonlocal interaction kernel estimation.
problem Estimating nonlocal interaction kernels in interacting particle systems.
method Introduced tamed least squares estimator (tLSE) achieving optimal convergence rate.
result Optimal minimax rate of convergence confirmed for β ≥ 1 / 4 β \geq 1/4 β ≥ 1/4 . Study minimax robustness in statistical estimation under Wasserstein contamination.
problem Adversarial perturbations in statistical data.
method Developed minimax theory for ℓ q r \ell_q^r ℓ q r losses under Wasserstein- r r r contaminations. result Exact minimax risk identified for joint contaminations in location estimation and prediction in linear regression.
The paper optimizes k-NN for distributed learning with minimax optimal performance.
problem Minimizing error rates in classification, regression, and density estimation.
method Optimal aggregation of fixed-k nearest neighbors from multiple subsets of data.
result Achieves minimax optimal error rates up to a logarithmic factor.
Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the…
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
Paper tackles adversarial attacks on nonparametric regression models.
problem Vulnerability of machine learning models to adversarial attacks in nonparametric regression.
method Establishes minimax rate and proposes adaptive estimators for robust nonparametric regression under adversarial L q L_q L q -risks. result Achieves minimax optimality and provides adaptive estimators for robust nonparametric regression.
Paper proposes robust estimators for GANs under Wasserstein contamination.
problem Robust estimation of distributions under contamination.
method Wasserstein GAN-based estimators for location, covariance, and regression.
result Proposed estimators are minimax optimal in many scenarios.
New estimator achieves minimax optimal risk in transfer learning.
problem Nonparametric regression with transfer learning.
method Confidence thresholding estimator and data-driven adaptive algorithm.
result Adaptive algorithm achieves minimax risk up to a logarithmic factor.
Paper tackles moment estimation under covariate shift with a two-stage algorithm.
problem Estimating moments under covariate shift when source and target distributions differ.
method Proposes a two-stage algorithm: first, an optimal estimator for the source distribution; second, likelihood ratio reweighting for calibration.
result Achieves minimax optimal bound for moment estimation.
Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.
problem Minimizing excess risk across all test distributions.
method Zeroth-order stochastic mirror descent algorithm for both smooth and non-smooth MERO.
result Converges at optimal rates of O ( 1 / t ) \mathcal{O}(1/\sqrt{t}) O ( 1/ t ) for estimates and optimization errors. Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.
problem High-dimensional stochastic linear bandits with sparse parameters.
method Three-stage arm selection algorithm using thresholded Lasso for estimation.
result Achieves exact minimax optimality in cumulative regret.
New research optimizes HSIC estimation rate for translation-invariant kernels.
problem Optimizing the rate of HSIC estimation for translation-invariant kernels.
method Proved minimax optimal rate of O ( n − 1 / 2 ) O(n^{-1/2}) O ( n − 1/2 ) for HSIC estimation. result Optimality of various HSIC estimators proven.
The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.
problem High-dimensional additive regression with heavy-tailed errors and transfer learning.
method Smooth backfitting estimator with local linear smoothing, followed by a two-stage estimation method.
result The method achieves the minimax optimal rate under certain conditions.
Score attack method provides a lower bound on privacy-constrained minimax risk.
problem Characterizing the optimality of privacy-constrained statistical models.
method Score attack based on tracing attack concept.
result Optimally lower bounds the minimax risk of estimating unknown model parameters.
Neural networks minimize error with shallow ReLU models for function estimation.
problem Estimating unknown functions from noisy data.
method Minimizing squared errors plus weight decay regularization.
result Neural network estimators are minimax optimal up to logarithmic factors.
Private KL distribution estimation improved with instance-optimality.
problem Minimizing KL divergence between true and estimated distributions.
method Construct minimax optimal private estimators, then focus on instance-optimality.
result Achieved instance-optimality up to constant factors for KL estimation.
Paper optimizes private PCA for covariance estimation in statistics.
problem Private estimation of covariance matrices and principal components.
method Developed differentially private estimators for spiked covariance model.
result Established minimax rates of convergence for principal components and covariance matrix estimation.
Optimal algorithm for linear bandits on ellipsoids with minimax regret bound.
problem Linear stochastic bandits on ellipsoids.
method Novel sequential procedure to estimate norm of parameters, followed by an explore-and-commit strategy.
result Regret bound matches minimax lower bound with multiplicative constant.
Paper shows MoM is optimal under adversarial contamination for certain distributions.
problem Optimality of MoM under adversarial contamination.
method Upper and lower bounds for MoM's error under adversarial contamination.
result MoM is (minimax) optimal for distributions with finite variance and infinite variance with finite absolute moments.
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
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.
We consider the problem of accurately estimating the reliability of workers based on noisy labels they provide, which is a fundamental question in crowdsourcing. We propose a novel lower bound on the minimax estimation error which applies to any estimation procedure. We further propose Triangular Estimation (TE), an al…
Develops shuffling gradient-based methods for nonconvex-concave minimax optimization.
problem Nonconvex-concave minimax optimization problems.
method Two shuffling gradient-based algorithms for nonconvex-linear and nonconvex-strongly concave settings.
result Achieves state-of-the-art oracle complexity in nonconvex optimization and best-known complexity bounds for nonconvex-strongly concave setting.
Paper optimizes estimation of quadratic functionals in nonparametric IV models.
problem Optimal estimation of a nonlinear functional in ill-posed inverse regression.
method Adaptive, minimax estimation using leave-one-out, sieve NPIV estimator with data-driven sieve dimension selection.
result Adaptive estimator achieves minimax optimal rate in various ill-posed cases.
New research sets the minimax lower bound for KSD estimation at sqrt(n).
problem Estimating goodness-of-fit using Kernel Stein Discrepancy (KSD) on high-dimensional spaces.
method Two complementary results proving the minimax lower bound of KSD estimation.
result The minimax lower bound of KSD estimation is n^(-1/2), indicating exponential difficulty with dimensionality.
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on n n n independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probabili…
Paper develops a method for estimating PFLM with minimized rates in high dimensions.
problem Estimating PFLM with minimized rates in high dimensions.
method Least square approach with mixed regularizations of function-norm and ℓ1-norm.
result Established optimal minimax rates of estimation for PFLM.
Paper studies minimax optimal regression using Laplacian smoothing over graphs.
problem Minimax optimal regression over Sobolev spaces.
method Laplacian smoothing on neighborhood graphs.
result Upper bounds match minimax optimal rates for first-order Sobolev class.
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in L q L_q L q -norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
Develops a minimax optimal estimator for system stability under distribution shift.
problem Ensuring system reliability under changes in the underlying environment.
method Minimax optimal estimation of stability defined in terms of acceptable performance degradation.
result Characterizes the minimax convergence rate and demonstrates practical utility.
Researchers develop optimal methods to estimate rough volatility parameters.
problem Statistical inference for rough volatility models with fractional Brownian motion.
method Established minimax lower bounds and designed wavelet-based procedures.
result Optimal speed of convergence n − 1 / ( 4 H + 2 ) n^{-1/(4H+2)} n − 1/ ( 4 H + 2 ) for estimating H H H . Study minimax rates for density estimation under Huber contamination and Besov IPM losses.
problem Minimax convergence rates of nonparametric density estimation under Huber contamination model with outliers.
method Re-scaled thresholding wavelet series estimator and GAN architectures.
result Achieves minimax optimal convergence rates under Besov IPM losses.
Study optimizes estimation of orthogonal and rotation matrices from noisy data.
problem Estimating orthogonal and rotation matrices from noisy data.
method Iterative polar decomposition algorithm initialized by spectral methods.
result Algorithm achieves optimal error rate of $(1+o(1)) rac{σ^2 d(d-1)}{2np}$ .
Bayesian histograms achieve optimal distribution estimation with minimal memory usage.
problem Efficiently estimating distributions with minimal memory footprint.
method Bayesian histograms for distribution estimation under Wasserstein distance.
result Bayesian histograms require fewer bins to achieve minimax optimality, reducing memory usage by a polynomial factor.
Diffusion models achieve nearly optimal distribution estimation in various spaces.
problem Theoretical limitations of diffusion modeling for distribution estimation.
method Analysis of approximation and generalization abilities of diffusion models in Besov spaces.
result Diffusion models achieve nearly minimax optimal estimation rates in total variation and Wasserstein distances.
GL-LowPopArt improves minimax-optimal estimation for trace regression.
problem Minimizing estimation error in generalized low-rank trace regression.
method Two-stage approach: nuclear norm regularization followed by matrix Catoni estimation.
result Achieves instance-wise optimal error bounds up to condition number.
Study optimizes shared singular subspace estimation from noisy matrices.
problem Estimating shared singular subspaces across multiple noisy matrices.
method Low-rank matrix denoising framework with Stack-SVD and novel estimators.
result Stack-SVD achieves minimax rate-optimality for identical shared subspaces, and novel estimators for partial sharing.
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of parameters are precisely non-zero. This excludes models where linear formulations…
New method estimates hidden binary mixture model centers efficiently.
problem Estimating centers in high-dimensional binary mixture models with hidden Markov structure.
method Proposes a minimax optimal procedure and an adaptive variant.
result Achieves optimal rate of order δ d / n + d / n \sqrt{δd/n} + d/n δ d / n + d / n . Preconditioned non-convex gradient descent improves noisy matrix estimation.
problem Estimating low-rank matrices from noisy measurements.
method Preconditioned non-convex gradient descent for noisy measurements.
result Preconditioned method converges to minimax optimal estimate at a linear rate.
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.