Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
LoCoV reduces portfolio optimization errors from sample covariance matrices.
problem Large errors in sample covariance matrix for optimal portfolio weights.
method LoCoV (low dimension covariance voting) algorithm to reduce these errors.
result LoCoV outperforms classical methods in portfolio optimization experiments.
Novel approach for SEM in small samples with p>n.
problem Small sample size and p>n issues in factor-based SEM. method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.
A new covariance estimator reduces dimensionality in high-dimensional undersized samples.
problem Challenges in estimating covariance matrices for high-dimensional data with fewer samples.
method Maximum Entropy Covariance (MEC) estimator that combines covariance matrices from different response categories.
result MEC estimator improves efficiency in dimension reduction methods like SIR and SAVE.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Improved sampling for Diffusion Models by accounting for covariance.
problem Sampling quality degradation in few-step Diffusion Models.
method Covariance-aware sampler using Tweedie's formula and Fourier-space decomposition.
result Consistently superior samples compared to state-of-the-art samplers.
Semi-supervised method boosts two-sample testing with covariate data.
problem Two-sample testing with covariate information.
method Semi-supervised kernel test with asymptotic normality.
result Higher asymptotic power compared to existing methods.
This paper explores how effective sample size, dimensionality, and model performance are related in covariate shift adaptation.
problem Understanding the relationship between effective sample size, dimensionality, and generalization in covariate shift adaptation.
method Building a unified theory connecting effective sample size, data dimensionality, and generalization in the context of covariate shift adaptation.
result Dimensionality reduction or feature selection can increase effective sample size, supporting the practice of reducing dimensionality before covariate shift adaptation.
Proposes SVI for covariate-shift generalization with sparse variable independence.
problem Covariate-shift generalization with limited data and unstable variables.
method Introduces sparsity constraint and combines reweighting and selection in an iterative way.
result Improves covariate-shift generalization performance on synthetic and real-world datasets.
How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and distributions supported in a centered Euclidean ball, we prove …
We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a 0−1 Bernoulli random variable. We analyze an unbiased covariance estimator under this mod…
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
Robust covariance testing requires significantly more samples in contaminated data.
problem Testing the covariance matrix of a high-dimensional Gaussian in the presence of contamination.
method We study the problem in the Huber's contamination model, distinguishing between the identity matrix and matrices far from it in Frobenius norm.
result The sample complexity of covariance testing increases dramatically to Ω(d2) in the contaminated setting. Estimates covariance matrices with correlations between samples.
problem Estimating large-dimensional covariance matrices with correlated samples.
method Generalized Marcenko-Pastur equation and Ledoit-Peche shrinkage estimator using random matrix theory and free probability. Developed an efficient algorithm based on Ledoit-Wolf kernel estimation.
result Efficient algorithm for estimating large covariance matrices with correlations.
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from least square, principal, iterative principal component, alpha or i…
The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for th…
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matri…
WeSpeR speeds up non-linear shrinkage for high-dimensional weighted covariance.
problem Computing non-linear shrinkage formulas for high-dimensional weighted sample covariance.
method Derive extit{WeSpeR} algorithm using asymptotic sample spectrum properties.
result Significantly speeds up non-linear shrinkage in dimensions higher than 1000.
Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.
problem Complexity of covariance matrix estimation for Gibbs distributions.
method Uses Markov chain Monte Carlo with conditions on the chain's spectral gap and Poincaré inequality.
result Achieves similar sample complexity as i.i.d. samples with better query complexity.
DACE estimates covariance from compressed data, improving accuracy.
problem Estimating covariance from large, distributed data.
method Data-aware weighted sampling for unbiased estimation.
result DACE provides more accurate covariance estimation under compression.
Proposes a new method to adapt to covariate shifts in supervised learning.
problem Covariate shift in training and testing samples with different marginal distributions.
method Minimax risk classification (MRC) approach that weights both training and testing samples.
result Significantly enhanced classification performance in synthetic and empirical experiments.
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples. The method allows for exact determination of the experimental spectru…
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
problem Uncertainty in estimating covariance matrix leads to unreliable hedge trades.
method Proposes two new estimators of the inverse covariance matrix using l2 and l1 norms.
result Portfolio formed using proposed estimators achieves substantial risk reduction and improved returns.
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…
Regularized EM algorithm improves GMM clustering in low sample settings.
problem Numerical instability and convergence issues in EM-GMM for low sample support.
method Regularized EM algorithm that maximizes penalized GMM likelihood, ensuring positive definiteness and structured covariance matrices.
result The regularized EM algorithm leads to better performing EM for structured covariance matrix models or low sample settings.
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…
Study improves treatment effect estimation using unlabeled covariates.
problem Estimating treatment effects with limited labeled data.
method Developed efficiency bounds and estimators for semi-supervised setting.
result Estimators using unlabeled covariates have lower asymptotic variance.
Exact minimax risk derived for linear prediction with sample covariance analysis.
problem Understanding the minimax risk in linear prediction under various covariate distributions.
method Exact minimax risk analysis, leveraging statistical leverage scores and PAC-Bayes techniques.
result The minimax risk is of order d/(n−d+1) for any covariate distribution, nearly matching the risk for Gaussian design. Efficiently estimates prediction error in regression with Gaussian covariates under privacy constraints.
problem Private regression with Gaussian covariates under differential privacy constraints.
method Sum-of-Squares framework combined with robust estimators.
result Sample-optimal private regression algorithm with optimal error rates.
The paper proposes AIS for Bayesian inversion of multioutput signals with covariance estimation.
problem Performing uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals.
method Adaptive Importance Sampling (AIS) scheme, split variables, frequentist approach for noise covariance, prior density over covariance matrix.
result Estimation of model parameters and covariance matrix of noise.
Optimizes sample reweighting to match laws under covariate shift using Wasserstein distance.
problem Matching laws of samples with different distributions under covariate shift.
method Minimizes Wasserstein distance between empirical measures of samples using Nearest Neighbors weights.
result Consistent reweighting leads to asymptotic convergence of empirical measures.
Study on estimating distances between covariance operators and Gaussian processes.
problem Estimating distances between covariance operators and Gaussian processes.
method Riemannian distances, concentration results for Hilbert space-valued random variables, RKHS covariance and cross-covariance operators.
result Both distances converge in the Hilbert-Schmidt norm and can be consistently and efficiently estimated.
We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor…
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.
Robustly estimates linear regression coefficients with adversarial and noisy data.
problem Estimating robust linear regression coefficients with adversarial and noisy data.
method Adversarial robust weighted Huber regression with polynomial computational complexity.
result Derives an estimation error bound that depends on the stable rank and condition number of the covariance matrix.
Regularized EM algorithm improves clustering performance with small sample sizes.
problem Performance reduction in EM algorithm due to small sample size and poorly conditioned covariance matrices.
method Regularized EM algorithm that uses prior knowledge to ensure positive definiteness of covariance matrices.
result The regularized EM algorithm outperforms standard EM in clustering tasks with small sample sizes.
The covariance matrix of a p-dimensional random variable is a fundamental quantity in data analysis. Given n i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of O(np2) operations. When n,p are large, this computation may be prohibitively slow. Moreover, …
The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.
problem Statistical validation of normal conditions in high-dimensional time series data.
method Generalizes the maximal deviation of sample autocovariances to high dimensions and applies Gumbel-type extreme value asymptotics.
result Gumbel-type extreme value asymptotics holds true for high-dimensional sample covariances.
The paper defines conditions for Gaussian process sample path regularity.
problem Lack of understanding of Gaussian process sample path regularity.
method Analyzes covariance kernels to determine sample path regularity.
result Necessary and sufficient conditions for Hölder regularity are provided.
New algorithm reduces sample complexity for sparse linear regression.
problem Sparse linear regression with correlated covariates and approximate dependencies.
method Polynomial-time algorithm that adapts the Lasso to tolerate approximate dependencies.
result Achieves near-optimal sample complexity for constant sparsity and ill-conditioned covariates.
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
Study extends bounds on sample covariance matrices with general dependence.
problem Quantitative bounds on sample covariance matrices with i.i.d. columns.
method Extends previous work on deterministic equivalent to rectangular random matrices with general dependence structure.
result Proves quantitative bounds involving dimensions and spectral parameter, including closer proximity to real positive semi-line.
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…
A new LDA model with covariates for mixed-membership clusters.
problem Modeling mixed-membership clusters in discrete data with covariates.
method Negative binomial regression embedded within LDA, slice sampling within Gibbs sampling.
result Model successfully retrieves true parameter values and predicts cluster abundances using covariates.
Study improves covariance estimation for SGD under Markovian data, matching best rates.
problem Improving covariance estimation for SGD in Markovian data settings.
method Online overlapping batch-means covariance estimator for SGD under Markovian sampling.
result Established convergence rates for covariance estimation under Markovian sampling.
Better signal detection in undersampled data using joint and cross covariances.
problem Detecting shared signals in high-dimensional data with limited samples.
method Analysis of three covariance matrices: individual, cross, and joint.
result Joint and cross covariance matrices detect signals earlier than individual covariances.
EiGLasso speeds up sparse Kronecker-sum covariance estimation.
problem Sparse Kronecker-sum inverse covariance estimation challenges in scalability and parameter identification.
method Newton's method combined with eigendecomposition of sample and feature graphs, approximating Hessian for speed.
result Two to three orders-of-magnitude speed-up on simulated and real-world data.