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.
Paper derives optimal shrinkage estimator for high-dimensional mean vectors.
problem Estimating high-dimensional mean vectors with shrinkage.
method Linear shrinkage estimator using random matrix theory.
result Optimal shrinkage estimator minimizes quadratic loss asymptotically.
New estimator for mean of random vector achieves sub-Gaussian performance.
problem Estimating the mean of a random vector with sub-Gaussian performance.
method Introduces a multivariate median-based estimator under the condition of finite second moment.
result Achieves purely sub-Gaussian performance with only second moment condition.
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.
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψ random vectors. Generalizes Barankin bound for vector cases in mean square error.
problem Achieving the lower bound of mean square error for vector estimates.
method Finite dimensional vector Riesz representation theorem and linear matrix inequality.
result Necessary and sufficient conditions for achieving the lower bound.
Smooth solutions found for modified mean curvature flow in Riemannian manifolds.
problem Existence of smooth solutions for modified mean curvature flow.
method A priori estimates for modified mean curvature flow in Riemannian manifolds with Killing vector field.
result Existence of smooth, entire, longtime solutions for modified mean curvature flow with smooth initial data.
New compression schemes save communication in distributed mean estimation.
problem Efficiently compressing vectors for mean estimation in a limited communication setting.
method Collaborative compression schemes that exploit vector similarities without requiring known correlations.
result Analysis shows varying error types with vector similarity.
Paper addresses robust sparse vector mean estimation under local differential privacy.
problem Challenges in defending poisoning attacks on multi-item users in LDP protocols.
method Randomized Projection with Clipping (RPC) to handle clipping bias and enhance robustness.
result Proposes a method that achieves comparable or better performance than existing methods under trusted environments and significantly enhances robustness under untrusted environments.
New linear spectral estimators improve phase retrieval accuracy.
problem Recovering vectors from magnitude measurements.
method Linear Spectral Estimators (LSPEs) for phase retrieval.
result LSPEs provide accurate initialization vectors and sharp error bounds.
Estimates mean of random vector with near-optimal error in all directions.
problem Estimating the mean of a random vector with direction-dependent accuracy.
method Proves existence of an estimator with near-optimal error in all directions under certain conditions.
result The estimator satisfies the error bound for all directions, with probability 1-δ.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
Physics-based method approximates mean curvature on surface meshes.
problem Estimating mean curvature on triangulated surfaces.
method Derives approximation from Young-Laplace equation and force balance.
result Approximation equivalent to discrete Laplace-Beltrami operator.
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.
A fast spectral algorithm estimates mean of heavy-tailed vectors efficiently.
problem Estimating the mean of heavy-tailed random vectors with optimal error bound.
method Spectral algorithm using eigenvector computations and novel hyperplane connection.
result Achieves optimal sub-gaussian error bound with improved runtime.
Study surfaces with parallel mean curvature in spheres, proving rigidity results.
problem Characterize surfaces with parallel mean curvature in unit spheres.
method Establish Simons-type integral identities and apply to rigidity and gap estimates.
result Obtain first two sharp endpoint gaps and rigidity estimates.
A study on distributed mean estimation with trade-offs between communication and accuracy.
problem Estimating the arithmetic average of distributed vectors with limited communication.
method Proposes a flexible family of randomized algorithms exploring the trade-off between communication cost and estimation error.
result Improves error rate to O(r/n) when communicating a single bit per coordinate, where r is the bit representation of a floating point value. A new method estimates population mean using labeled and unlabeled data.
problem Estimating population mean with limited labeled data.
method Semi-supervised inference framework, least squares method.
result Proposed estimators outperform ordinary sample mean.
Faster mean estimation with sub-Gaussian error bounds.
problem Estimating the mean of a random vector with optimal statistical efficiency.
method An estimator for the mean of a random vector in R^d with optimal statistical efficiency and sub-Gaussian error bounds.
result Achieves optimal statistical efficiency with sub-Gaussian error bounds and a significantly faster runtime.
New algorithms reduce communication for sparse mean estimation in noisy distributed systems.
problem Sparse normal means estimation with limited communication in a distributed setting.
method Two distributed algorithms for estimating a sparse mean vector with sublinear communication.
result Correct support of the sparse mean can be recovered with significantly less communication than previously required.
New diameter estimate on manifolds with positive Bakry-Émery Ricci tensor.
problem Estimating the diameter of manifolds with specific curvature conditions.
method Using generalized mean curvature comparison on excess function.
result Sharper diameter estimate than previous results.
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.
Paper improves distributed mean estimation and variance reduction without relying on input norm.
problem Distributed mean estimation and variance reduction with large input norms.
method Quantization and lattice theory connection for improved error bounds.
result Output error bounds depend only on input distance, not norm.
Method compares sentences by cosine similarity of vector projections.
problem Measuring semantic similarity of sentences.
method Cosine similarity of vector projections of sentence groups.
result Advantages over existing methods in preserving word order and syntactic connections.
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.
Stochastic trace estimation with tensor train random vectors
problem Stochastic trace estimation for large-scale matrices
method Gaussian random tensor train vectors
result Median-of-means variant achieves dimension-independent guarantees
We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given α-Hölder continuous vector field, then we show C^{2,α} regularity almost everywhere.
The paper proposes a method to improve forecast combination accuracy using portfolio theory.
problem Improving forecast accuracy by combining multiple forecasts.
method Generates forecast combinations using a portfolio analogy, allowing negative weights for hedging.
result Demonstrates improved performance in weighted random forest forecasts.
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.
This paper improves multi-task estimation in distributed networks using APA.
problem Simultaneous estimation of multiple vectors in collaborative networks.
method Multi-task diffusion strategies based on Affine Projection Algorithm (APA).
result Improved performance in terms of convergence rate and steady state EMSE.
Paper proposes new estimators for error variance in high-dimensional linear models.
problem Estimating error variance in high-dimensional linear models.
method Proposes natural lasso and organic lasso estimators.
result Natural lasso estimator maximizes a penalized likelihood objective and has provably good performance.
VB approximates posterior mean perfectly in linear Gaussian VAR models.
problem Unknown approximation error of VB in VAR models.
method Derive approximation error in terms of mean, mode, variance, predictive density, and KL divergence.
result VB approximates posterior mean perfectly.
New framework for regression trees with multivariate response and dynamic mean vectors.
problem Characterizing and implementing regression trees for multivariate responses.
method High dimensional model with dynamic mean vectors over multi-dimensional change axes.
result Optimal rate of convergence and asymptotic valid confidence intervals for change points.
New method estimates mean from noisy data with few outliers.
problem Estimate mean from noisy data with few outliers.
method Iterative multi-filtering approach.
result Achieves near-optimal error with practical efficiency.
Maps between 2D spaces evolve under area-decreasing conditions.
problem Understanding the evolution of maps under area-decreasing constraints.
method Mean curvature flow of the graph of a map between 2D Euclidean spaces.
result Existence and uniform decay estimates for the evolving submanifold.
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …
A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they are critical points of some natural functionals. In this paper, we su…
EM algorithm converges in 10 steps for 2 Gaussian mixtures.
problem Estimating mixtures of two Gaussians with known covariance matrices.
method Expectation-Maximization (EM) algorithm with convergence guarantees.
result EM converges geometrically in 10 steps for 2 Gaussian mixtures.
The paper studies f-stability of hypersurfaces in gradient Ricci solitons.
problem Estimating the f-stability index of constant weighted mean curvature hypersurfaces. method Analyzes hypersurfaces in shrinking gradient Ricci solitons with parallel fields.
result Provides an estimate for the f-stability index and necessary conditions for equality. New framework reduces private mean estimation error with optimal efficiency.
problem Locally private mean estimation of high-dimensional vectors.
method ProjUnit framework: random projections, normalization, and optimal algorithm execution in lower dimensions.
result Optimal error up to a 1+o(1)-factor with computational efficiency and low communication complexity.
Robust GQDA improves classification accuracy in non-Normal data.
problem Non-robustness of GQDA under data contamination.
method Introduced robust estimators for mean vector and dispersion matrix.
result Robust GQDA classifiers perform significantly better in real data applications.
High codimension submanifolds evolve to convex shapes, leading to smooth limiting flows.
problem Evolution of high codimension submanifolds in Rn+k. method Proving asymptotic convexity and using it to show convergence to a smooth limiting flow.
result High codimension submanifolds evolve to convex shapes, and at singular times, rescaling converges to a smooth limiting flow.
We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is obtained. Then, we completely classify the proper biharmonic submanifolds in spheres w…
Proposes a new framework to optimize portfolios with reduced estimation errors.
problem Estimation errors in multiperiod mean-variance portfolio optimization.
method Reference-regulated multiperiod mean-variance (RRMV) framework.
result Improves portfolio stability and out-of-sample Sharpe ratios.
The paper proves inequalities and formulas for submanifolds in specific warped product manifolds.
problem Understanding geometric properties of submanifolds in warped product manifolds.
method Proving linear isoperimetric inequalities and monotonicity formulas for submanifolds with bounded mean curvature vector.
result Lower bound estimates for the volume of submanifolds in terms of the warping function.
Efficiently estimates private least squares with linear error growth.
problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.
This paper introduces a novel clustering algorithm for heteroscedastic Gaussian data without needing to know the number of clusters.
problem Clustering heteroscedastic Gaussian data without prior knowledge of the number of clusters.
method Introduces a novel cost function and fixed-point analysis to estimate centroids, introduces Wald kernel for measurement plausibility, and derives CENTRE-X algorithm.
result CENTRE-X algorithm can estimate centroids without prior knowledge of the number of clusters and performs comparably to standard algorithms K-means and Mean-Shift.
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.