New method estimates matrix trace using machine learning with fewer vectors.
problem Estimating matrix trace when explicit form is not known.
method Uses machine learning to determine a small number of probing vectors for matrix multiplication to a vector.
result Precision of trace estimates with 10 probing vectors is similar to 10000 random vectors.
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.
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
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 constructs L2 estimates for flat vector bundles and generalizes Prékopa's theorem.
problem Constructing L2 estimates for flat vector bundles. method Using Hörmander's L2-estimate for the operator d on a flat vector bundle over a p-convex Riemannian manifold. result Generalizes Prékopa's theorem in convex analysis.
This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when p≫N. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, G−1 canonical vectors can be considered if the number of groups is G. In…
Paper generalizes gradient estimate for vector fields up to higher step.
problem Generalizing gradient estimates for vector fields up to higher step.
method Using generalized curvature-dimension inequality, derived Li-Yau gradient estimate.
result Obtained Li-Yau gradient estimate for CR heat equation.
We analyze how errors in interbank liabilities affect the clearing vector in financial systems.
problem Estimation errors in interbank liabilities can lead to inaccuracies in the clearing vector, impacting risk assessments.
method We quantify the sensitivity of the clearing vector to estimation errors in the interbank liabilities matrix using a basis for permissible perturbations.
result We derive analytical solutions for the maximal deviations of the clearing vector and compute upper bounds for worst-case perturbations.
New method estimates Gaussian vector functions more efficiently.
problem Estimating functions of Gaussian vectors with high dimensions.
method Combines randomized dimension reduction and PCA.
result Algorithm outperforms Monte Carlo method by a factor of d.
Estimates on symmetric spaces derived from Euclidean results.
problem Proving estimates on symmetric spaces of non-compact type.
method Duality estimate between vector fields and critical Sobolev space solutions.
result Sharp Calderon-Zygmund estimate for Poisson's equation solutions.
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.
New characterizations of curvature operators for specific forms via L2-estimates.
problem Characterizing semi-positive and semi-negative curvature operators for (n,q) and (p,n)-forms. method Using L2-estimates to characterize curvature operators for (n,q) and (p,n)-forms. result New characterizations of Nakano semi-positivity and semi-negativity.
The paper develops quantitative estimates for holomorphic sections over bounded domains.
problem Establishing precise inequalities for holomorphic sections over bounded domains.
method Develops Sobolev-type inequalities and applies them to holomorphic sections of Hermitian vector bundles.
result Quantitative Carleman-type estimates for holomorphic sections are derived, improving on previous non-quantitative results.
Estimates eigensections norms on Riemannian bundles.
problem Bounding the L∞-norm of eigensections. method Using diameter, dimension, Ricci and bundle curvature.
result Eigensections with small eigenvalues are almost parallel.
We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.
The study proves that conformal Killing vector fields on manifolds with positive Ricci curvature are non-trivial.
problem Investigating conformal Killing vector fields on manifolds under curvature pinching conditions.
method Establishing a new Bochner-type identity and using Moser iteration for gradient estimates.
result Conformal Killing vector fields are non-trivial on manifolds with positive Ricci curvature.
Proposes a DOA estimation method using IVs and DNNs for noise and reverberation reduction.
problem Accuracy of IV-based DOA estimation degrades due to noise and reverberation.
method Combines IV-based DOA estimation with DNNs for denoising and dereverberation.
result Average DOA error of 0.528 degrees, outperforming conventional methods.
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.
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.
Study shows curvature of Hermitian-Yang-Mills flow is uniformly bounded.
problem Curvature estimate of Hermitian-Yang-Mills flow on holomorphic vector bundles.
method Uniform curvature bound demonstrated in a simple case.
result Curvature of evolved Hermitian metric is uniformly bounded.
New algorithms reduce computational burden for principal support vector machines.
problem High computational cost of principal support vector machines for large datasets.
method Two distributed estimation algorithms for principal support vector machines.
result Statistical efficiency is maintained with distributed algorithms.
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. 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.
The paper proposes cluster-based James-Stein estimators to improve parameter estimation in high dimensions.
problem Estimating high-dimensional parameters from noisy observations with significant risk reduction over ML.
method The approach involves clustering data components and shrinking them towards common attractors to reduce risk.
result The proposed estimators give significant risk reduction for a wide range of parameters, especially in high dimensions.
Estimator Vectors learns OOV word embeddings using subword and context clues.
problem Lack of OOV word representations in neural network models.
method Jointly learns word, subword, and context clue representations.
result Strong estimates for OOV words via combined subword and context clue embeddings.
We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds and Hörmander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial diffe…
Estimates small eigenvalues for geometrically finite manifolds.
problem Estimating small eigenvalues of Schrödinger operators.
method Geometrically finite manifolds, Riemannian vector bundles.
result Estimates the number of small eigenvalues.
The paper characterizes positivity of holomorphic vector bundles via Lp-estimates and extensions.
problem Characterizing positivity of holomorphic vector bundles using Lp-estimates and extensions. method Introducing four conditions for Hermitian (or Finsler) vector bundles and characterizing Nakano and Griffiths positivity.
result Characterization of Nakano and Griffiths positivity via specific Lp-conditions. Study on dimensions of Killing vector fields on gradient Ricci solitons.
problem Estimating dimensions of Killing vector fields on gradient Ricci solitons.
method Analyzes the structure of gradient Ricci solitons to estimate dimensions of Killing vector fields.
result Maximal dimension of Killing vector fields on irreducible non-trivial gradient Ricci solitons.
The paper proposes a new model to analyze directed networks and accurately estimate community memberships.
problem Modeling and estimating community memberships in directed networks with heterogeneous degrees.
method Directed Degree Corrected Mixed Membership (DiDCMM) model and DiMSC algorithm.
result The proposed DiMSC algorithm is asymptotically consistent and provides error bounds for community membership vectors.
Study robust covariance estimation in large data with concentrated vectors.
problem Estimating robust covariance in large data with concentrated vectors.
method Fixed point of a contracting function using stable semi-metric and concentration of measure.
result Existence and uniqueness of robust estimator with evaluated limiting spectral distribution.
This paper improves covariance estimation with minimal data.
problem Estimating covariance from few compressive measurements.
method Back-projections of compressive samples for consistent estimation.
result Single linear measurement suffices for consistent covariance estimation.
This paper extends the single index model to handle nonlinear relationships.
problem Nonlinear relationships in regression models.
method Exploits conditional distribution over function-driven partitions and uses linear regression for local estimation of index vectors.
result The method provides theoretical guarantees for estimation and prediction, and outperforms state-of-the-art methods.
New empirical Bayes estimator outperforms soft-thresholding for high-dimensional sparse vectors.
problem Estimating high-dimensional sparse vectors from noisy observations.
method Empirical Bayes shrinkage estimator using a Bernoulli-Gaussian prior.
result Hybrid estimator outperforms soft-thresholding in compressed sensing applications.
Efficient method for resampling problems using vector approximate message passing.
problem Computational demand in resampling techniques for statistical inference and ensemble learning.
method Combination of replica method from statistical physics and vector approximate message passing from information theory.
result Fast convergence and high approximation accuracy for variable selection problems.
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.
Active covariance estimation using random sub-sampling of variable subsets.
problem Estimating covariance matrices for partially observed random vectors.
method Unbiased covariance estimator under a model of partially observed variables and active learning framework.
result Derivation of error bounds revealing relations between sub-sampling probabilities and covariance matrix entries.
Improved estimation of VAR-Moving Average models using GLS.
problem Estimating VAR-Moving Average models efficiently.
method Use generalized least squares (GLS) for each fixed moving average polynomial.
result Likelihood function format similar to VAR models, allowing maximum likelihood estimation.
The paper tackles estimating vectors from binary comparisons, providing bounds and adaptive strategies.
problem Estimating a vector from binary comparisons of preference.
method Theoretical bounds and adaptive strategies for estimating vectors from noisy and randomized comparisons.
result Stable embedding of the space of target vectors and significant gains from adaptive distribution changes.
Estimates box dimension of fractal interpolation surfaces using oscillation vectors.
problem Estimating the complexity of fractal interpolation surfaces.
method Defined vertical scaling matrices and used them to relate oscillation vectors of different levels.
result Obtained the box dimension of generalized affine fractal interpolation surfaces.
Characterizes curvature positivity for Riemannian metrics on flat vector bundles.
problem Characterizing Nakano positivity of Riemannian flat vector bundles.
method Using solvability of the d equation with specific L2 estimates and inspired by recent works on Hermitian holomorphic vector bundles. result Alternative proof of matrix-valued Prekopa's theorem.
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
Unsupervised matching method for relational data without alignment info.
problem Matching objects in different relational datasets without correspondence info.
method Model latent vectors, estimate by likelihood, project onto shared space.
result Preserves structural information in latent vectors across datasets.
New characterization of Riemannian metric positivity and L2 estimates for d operator.
problem Characterize positivity of Riemannian metrics and L2 estimates for d operator. method Apply L2 technique developed by Deng-Ning-Wang-Zhou, new characterizations given. result Prove new results parallel to Liu-Yang-Zhou's answer to Lempert's question.
Bayesian SVM method speeds up big data predictions.
problem Efficiently predicting with big data and uncertainty.
method Stochastic variational inference and inducing points.
result Faster than competing Bayesian methods, scalable to millions of data points.
Estimates parameters of a rectified Gaussian distribution using ReLU networks.
problem Estimating parameters of a rectified Gaussian distribution from i.i.d. samples.
method Simple algorithm using O(1/ε2) samples and O(d2/ε2) time. result Estimates distribution up to ε in total variation distance. The paper provides estimates for flows on Riemannian manifolds using truncated expansions.
problem Quantifying the relationship between flows on Riemannian manifolds and their truncated logarithms.
method Using truncated versions of the Magnus and Baker-Cambel-Hausdorff-Dynkin expansions.
result Quantitative estimates between flows and their truncated logarithms.