New estimator reduces kernel mean estimation error.
problem Kernel mean estimation in reproducing kernel Hilbert spaces.
method Corrupt data with known distributions and estimate kernel mean under the corrupted distribution.
result The marginalized kernel mean estimator achieves lower estimation error.
New collaborative algorithm improves personalized mean estimation in online settings.
problem Online estimation of means from multiple, possibly overlapping distributions.
method Novel collaborative strategy for active querying and mean estimation.
result Algorithm improves mean estimates through communication among agents.
Novel mean estimation method under user-level differential privacy reduces noise in continual mean estimates.
problem Maintaining accurate running mean estimates under user-level differential privacy.
method Developed a novel mean estimation specific factorization under approximate differential privacy.
result Achieved asymptotically lower mean-squared error bounds in continual mean estimation.
Derives Hessian estimates for Lagrangian mean curvature equation.
problem Lagrangian mean curvature equation with supercritical phase and bounded second derivatives.
method Derives a priori interior Hessian estimates.
result Hessian estimates for Lagrangian mean curvature equation.
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…
Estimates mean curvature flow with geometric bounds.
problem Controlling mean curvature flow dynamics.
method Pointwise estimate using initial geometry and jHAj bound.
result Extension theorem and blowup rate estimate of HA.
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analy…
New method improves mean estimation for heavy-tailed data.
problem Estimating mean of heavy-tailed distributions.
method Median-of-Means (MoM) with symmetrization technique.
result Improved sample complexity bound for mean estimation.
Develops a computationally tractable differentially private mean estimator called the balloon mean.
problem Robust mean estimation in the presence of outliers and heavy-tailed distributions.
method Iterative clipping procedure over Mahalanobis balls.
result Balloon mean is robust to outliers and outperforms existing estimators in contaminated settings.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
This work extends Ledoit-Wolf shrinkage to unknown mean covariance estimation.
problem Large dimensional covariance matrix estimation with unknown mean under Kolmogorov asymptotics.
method Extending Ledoit-Wolf linear shrinkage to translation-invariant estimators, proving their convergence properties.
result A new estimator outperforms other standard estimators empirically.
A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this e…
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.
New winsorized mean improves robustness to up to 50% contamination.
problem Improving robustness of mean estimation in the presence of outliers.
method Outlyingness-induced winsorized mean approach.
result Achieves up to 50% contamination robustness with sub-Gaussian performance.
Robustly estimates mean with quantized data and corruption.
problem Mean estimation under quantization and adversarial corruption.
method Constructs multivariate robust estimators in two settings.
result Optimal estimators up to logarithmic factors.
The paper estimates the volume of singular points in evolving surfaces.
problem Estimating the volume of singular points in evolving surfaces.
method Uniform and sharp volume estimates for singular sets of mean curvature flows.
result Uniform and sharp volume estimates for singular sets of mean curvature flows.
Eigenvalue estimate for shrinkers in mean curvature flow.
problem Eigenvalue estimates on shrinkers for mean curvature flow.
method Generalized earlier work of Ding and Xin to noncompact cases.
result Eigenvalue estimate holds on every properly embedded shrinker.
Paper proposes robust gossip algorithms for mean and trimmed mean estimation.
problem Vulnerability of mean-based gossip algorithms to malicious nodes.
method Developed extsc{GoRank} for rank estimation and extsc{GoTrim} for trimmed mean estimation.
result Established convergence rates for rank and trimmed mean estimation.
Paper proves gradient estimates for Lagrangian mean curvature equation.
problem Proving gradient estimates for Lagrangian mean curvature equation.
method Interior gradient estimates for critical and supercritical Lagrangian mean curvature equation.
result Solves Dirichlet boundary value problem for critical and supercritical Lagrangian mean curvature equation.
Robustly estimates mean in incomplete data with corrupted examples.
problem Estimating mean in data with missing values and outliers.
method Algorithms for robust estimation with optimal error guarantees in nearly-linear time.
result Information-theoretically optimal error guarantees for mean estimation.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Quantitative estimate for curvature in mean curvature flow.
problem Estimating curvature in mean curvature flow.
method Proving a curvature estimate for smooth convex ancient flows.
result Curvature grows at most quadratically in terms of rescaled extrinsic distance.
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.
Unified estimates for mean curvature in Lorentz-Minkowski space.
problem Estimating mean curvature for space-like and time-like graphs.
method Using gradient bounds to derive Heinz-type estimates.
result Unified vanishing theorem for mean curvature of constant mean curvature graphs.
New method estimates robust mean in high dimensions with minimized outliers.
problem Estimating the mean in high dimensions when a fraction of data is corrupted.
method Formulating the problem as ℓ0-norm minimization under second moment constraints, and using ℓ1 and ℓp minimization techniques. result The proposed method achieves order optimal robust mean estimation and significantly outperforms existing methods.
Estimates mean of distributed vectors with sparsification and spatial/temporal correlations.
problem Estimating mean of high-dimensional vectors distributed across nodes with low communication cost.
method Modifies decoding method to leverage spatial and temporal correlations in sparsified vectors.
result Estimators consistently outperform more sophisticated sparsification methods.
Develops a computationally tractable high-dimensional differential privacy estimator.
problem Differential privacy in high dimensions is computationally intractable.
method Combines high-dimensional robust statistics with differential privacy techniques.
result A computationally tractable algorithm with dimension-independent privacy loss.
Paper proposes a new UCB approach for estimating maximum mean.
problem Estimating the maximum mean in various applications.
method Upper Confidence Bound (UCB) approach with adaptive sampling.
result LSA estimator shows faster bias decay compared to GA.
Estimates multiple means in high dimensions using convex combinations.
problem Estimating multiple multi-dimensional means from samples.
method Convex combinations of empirical means with data-dependent weights.
result Our methods asymptotically approach oracle (minimax) improvement.
Study on estimating Gaussian mean from coarse data, resolving identifiability and computational efficiency questions.
problem Estimating the mean of a Gaussian distribution from coarse data (sets containing true samples rather than exact values).
method Analyzes the conditions for mean identifiability and computable estimation under convex partitions.
result Resolves the identifiability and computational efficiency questions for Gaussian mean estimation from coarse data.
Sharp estimate for flow in any dimension.
problem Interior gradient estimate for graphical mean curvature flow.
method Proving sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension.
result Generalized result in arbitrary codimension.
The paper proves Hessian estimates for specific geometric flows.
problem Proving interior Hessian estimates for specific geometric flows.
method Proved interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow.
result Extended results to a broader class of Lagrangian mean curvature type equations.
Sharp curvature estimates for mean curvature flow in spheres.
problem Understanding the behavior of surfaces evolving under mean curvature flow in spheres.
method Proving asymptotically sharp curvature pinching estimates and using them to derive derivative and convexity estimates.
result Partial classification of singularity models and new rigidity results for ancient solutions.
Efficiently estimates mean in contaminated Gaussian data with near-optimal sample complexity.
problem Robust mean estimation in the presence of mean-shift contamination.
method First computationally efficient algorithm with near-optimal sample complexity and polynomial-time running.
result Approximates the target mean to any desired accuracy with constant fraction of outliers tolerated.
The estimate of a Multiperiod probability of default applied to residential mortgages can be obtained using the mean of the observed default, so called the Mean of ratios estimator, or aggregating the default and the issued mortgages and computing the ratio of their sum, that is the Ratio of means. This work studies th…
Study examines mean estimation in high dimensions with small data.
problem Efficiently estimating mean in high-dimensional data with limited data size.
method Extensive experimentation of various mean estimation techniques.
result Developed robust methods for mean estimation with low data size.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
New method for estimating median and mean with high probability privacy.
problem Estimating median and mean with differential privacy.
method Propose, Test, Release (PTR) mechanism with concentration inequalities.
result First sub-Gaussian high probability bounds for differentially private median and mean estimation.
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function f, consistent estimators of the mean embedding of a random variable X lead to consistent estimators of the mean embedding of f(X). For Matérn ke…
The paper estimates area and volume for spacetimes with integral mean curvature bounds.
problem Estimating area and volume for spacetimes with specific curvature conditions.
method Using strong energy condition and norms of second fundamental form/mean curvature.
result Established area and volume estimates for spacetimes.
Simple private estimators for mean and covariance outperform existing methods.
problem Private estimation of mean and covariance at small sample sizes.
method Differentially private estimators for multivariate sub-Gaussian data.
result Asymptotic error rates match theoretical bounds and outperform previous methods.
Study proves rigidity theorems for ancient solutions to mean curvature flow with convex image.
problem Rigidity of ancient solutions to mean curvature flow with convex Gauss image.
method Refined curvature estimates.
result Better rigidity theorems for ancient solutions in higher codimension.
Paper proves estimates for Lagrangian flow singularities.
problem Understanding Lagrangian flow singularities.
method Interior a priori estimates and Jacobi inequality.
result Proves estimates for supercritical Lagrangian phase.
Paper proposes a 1-bit mean estimation method with near-optimal sample complexity.
problem Distributed mean estimation with 1-bit communication constraints.
method Randomized and sequentially-chosen interval queries to estimate mean.
result Sample complexity bound matches minimax lower bound with logarithmic factors.
Improved multi-task averaging reduces mean squared error in high-dimensional data.
problem Joint estimation of multiple distributions using independent data sets.
method Exploits similarities between tasks by shrinking naive estimators towards local averages.
result The method provides a significant reduction in mean squared error, especially in high-dimensional spaces.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².