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.
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 establishes non-asymptotic learning bounds for the DR covariate shift adaptation.
problem Distribution shift between training and test domains in machine learning.
method Doubly-robust (DR) estimator combining density ratio estimation and pilot regression model.
result First non-asymptotic learning bounds for DR covariate shift adaptation.
Federated learning method improves covariate shift adaptation for missing target values.
problem Missing target values in federated learning.
method Federated covariate shift adaptation algorithm for missing target output values.
result Asymptotically unbiased and efficient algorithm for federated learning.
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.
The paper proves asymptotic normality for multinomial logistic regression on null covariates.
problem Classical asymptotic normality results fail in high-dimensional multinomial logistic models.
method Developed asymptotic normality and chi-square results for multinomial logistic MLE on null covariates.
result Validated new methodology to test feature significance in high-dimensional classification problems.
Two new covariance estimators for ROOT-SGD improve statistical inference.
problem Uncertainty measurement for ROOT-SGD's normal distribution estimator.
method Developed two covariance estimators: plug-in and Hessian-free.
result Hessian-free estimator is asymptotically consistent and Hessian-free.
New method predicts sets under unknown covariate shift with high confidence.
problem Adapting to unknown covariate shift in prediction sets.
method PredSet-1Step, a flexible distribution-free method.
result Achieves asymptotic probably approximately correct coverage.
Extends covariance estimation with multiple targets for better performance.
problem Improving covariance estimation for multiple targets.
method Combines multiple constant matrices with sample covariance matrix, derives estimators and proves convergence.
result The multi-target linear shrinkage estimator outperforms other estimators in various situations.
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…
Paper develops methods for estimating GLMs and SNR under proportional asymptotics.
problem Estimation of regression coefficients and SNR in high-dimensional GLMs.
method Method-of-Moments type estimators that bypass nuisance function estimation.
result Consistent and asymptotically normal estimators derived for targets of inference.
Study on linear regression with dependent covariates, proving universality and error characterization.
problem Linear regression with dependent covariates in high-dimensional settings.
method Analysis of ridge regression performance, Gaussian universality theorem, spectral properties of covariance matrices.
result Asymptotic performance of ridge regression is invariant under non-Gaussian covariates with preserved mean and covariance.
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.
New method balances covariates for stable causal survival effect estimation.
problem Estimating causal survival effects in data with conditionally-independent censoring.
method Covariate-balancing approach to empirically stable and asymptotically efficient estimation.
result Validated theoretical results in synthetic and semi-synthetic data.
The paper analyzes the risk of a least squares estimator under a spike covariance model.
problem Risk analysis of the least squares estimator under a spike covariance model.
method Assumes spike covariance matrices, studies risk as d / n i g h t a r r o w ∞ d/n
ightarrow \infty d / ni g h t a r r o w ∞ . result Risk of the minimum norm least squares estimator vanishes compared to the null estimator.
Simple bounds for covariance and Gram matrices across various settings.
problem Capturing the behavior of smaller eigenvalues in covariance and Gram matrices.
method General-purpose theorem converting uniform bounds into relative bounds.
result Sharper control of eigenvalues across the spectrum.
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
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.
This study optimizes covariate density and propensity score for efficient ATE estimation.
problem Efficiently estimating average treatment effects (ATEs) with minimal variance.
method Adaptive experiment optimizing both covariate density and propensity score.
result Proposed method minimizes the semiparametric efficiency bound for ATE estimation.
Paper develops an online covariance estimator for nonsmooth stochastic approximation problems.
problem Estimating covariance in nonsmooth, potentially non-monotone settings.
method Online batch-means covariance matrix estimator.
result Estimator achieves convergence rate of O ( d n − 1 / 8 + ε ) O(\sqrt{d}n^{-1/8+\varepsilon}) O ( d n − 1/8 + ε ) . Paper develops statistical tests for covariance matrix regression on manifold.
problem Regression with random covariance matrices in Fréchet space.
method Develops Wasserstein F-tests for Bures-Wasserstein manifold.
result Asymptotic null distribution and power of the test.
Paper proposes an online estimator for covariance matrix of SGD iterates.
problem Quantifying variability and randomness of SGD-based estimates in online learning.
method Proposes a fully online estimator for covariance matrix of ASGD using SGD iterates.
result Establishes consistency of the online estimator and shows comparable convergence rate to offline methods.
Paper presents a new framework for covariance matrix estimation with geometric insights.
problem Challenges in covariance matrix estimation, especially in finding suitable models and efficient estimation methods.
method General framework for linear restrictions on different transformations of the covariance matrix, including matrix logarithm and its inverse.
result Yields an M M M -estimator with M M M -estimation allowing for straightforward asymptotic and finite sample analysis. New estimator handles covariate shift with closed-form solution and super-efficiency.
problem Handling covariate shift in missing data and causal inference problems.
method Minimum Wasserstein distance estimation framework.
result Closed-form expression and super-efficiency relative to semiparametric efficient estimator.
Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.
problem Efficiency in estimating treatment or policy effects in causal inference.
method Outcome-adapted AutoDML estimator that uses a shared covariate representation that is predictive of the outcome but not the Riesz representer.
result Outcome-adapted AutoDML estimator is asymptotically more efficient than baseline AutoDML.
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
New method calibrates asynchronous, error-prone covariates for longitudinal data.
problem Estimation biases and slow convergence in analyzing time-varying covariates with measurement error.
method Functional calibration approach based on functional principal component analysis.
result Asymptotically unbiased and consistent estimators for time-invariant coefficients; optimal convergence rate for time-varying coefficients.
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed domain (typically arising in spatial data analysis). We propose a detection method …
We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase sp…
New insights into how high-dimensional models handle covariate shifts.
problem Covariate shift in high-dimensional random feature regression.
method Exact high-dimensional asymptotics of random feature regression under covariate shift.
result Overparameterized models exhibit enhanced robustness to covariate shift.
The paper proposes a method to estimate treatment effects using CAR designs with additional covariates.
problem Estimating distributional treatment effects in CAR designs with additional covariates.
method Flexible distribution regression framework that incorporates additional covariates using machine learning methods.
result The proposed estimator attains the semiparametric efficiency bound for distributional treatment effects under CAR.
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.
problem Understanding the asymptotic and non-asymptotic properties of stochastic approximation procedures.
method Detailed analysis of linear stochastic approximation with Polyak-Ruppert averaging, focusing on asymptotic and non-asymptotic properties.
result Proves CLT and non-asymptotic concentration inequality for averaged iterates, providing refined understanding of linear stochastic approximation.
Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
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.
Efficiently estimates models with many variables using minimal communication.
problem Estimating models with a growing number of variables efficiently.
method Two rounds of communication to achieve asymptotically efficient estimator.
result Asymptotically efficient estimator for large-scale distributed data.
The paper develops time-uniform inference methods for stochastic approximation parameters.
problem Statistical inference for parameters in stochastic approximation problems.
method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.
result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.
Improved LDA using a nonlinear covariance estimator for better performance.
problem Inefficient LDA when data covariance is ill-conditioned.
method Regularized LDA with a positive semidefinite ridge-type estimator of the inverse covariance matrix.
result The proposed NL-RLDA classifier outperforms state-of-the-art methods across multiple datasets.
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect…
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing…
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.
In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we prove that decay of sectional curvature to -1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder …
Characterizes test error in learning with deep, structured feature maps.
problem Characterizing test error in learning with deep, structured feature maps.
method Asymptotic analysis of feature covariance and population covariance.
result Closed-form formula for feature covariance in Gaussian rainbow neural networks.
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.
Paper tackles unbounded density ratio estimation for covariate shift adaptation.
problem Understudied challenge in statistical learning: unbounded density ratios.
method Three-step estimation method: relative density ratio, truncation, and transformation.
result Established rigorous convergence guarantees for density ratio and regression estimators.
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the volume of domains on a submanifold of general codimension, determined by the inter…
The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…