Self-distillation optimally improves model performance in spiked covariance models.
problem Improving model performance in spiked covariance models.
method Developed spectral shrinkage estimators and analyzed self-distillation.
result Self-distillation achieves optimal performance among spectral shrinkage estimators for spiked covariance matrices.
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
The paper calibrates shrinkage covariance estimators for spectral functionals in high dimensions.
problem Calibrating shrinkage covariance estimators for spectral functionals in high dimensions.
method Derives first-order null laws, distribution-free Davis-Kahan bands, and calibrated tests for spectral functionals under shrinkage.
result Calibrated tests and intervals for spectral functionals are provided, addressing the issue of estimation noise and shrinkage bias.
Spectral deconfounding improves machine learning models by reducing hidden confounding effects.
problem Machine learning models can be misled by hidden confounders, leading to unreliable predictions.
method Develops a nonlinear spectral deconfounding framework for gradient boosting that modifies boosting dynamics to slow down in confounding-aligned directions.
result Spectrally deconfounded boosting improves estimation of the target function under hidden confounding and is more scalable.
New regularization method corrects over-shrinkage in small data regression.
problem Over-shrinkage in small data regression leading to underfitting.
method Negative-capable ridge family that permits negative regularization.
result Negative regularization acts as controlled anti-shrinkage, increasing effective complexity.
EigenBayes: A fast, adaptive Bayesian shrinkage approach for high-dimensional matrix factorization
problem Choosing the latent dimension k in factor models method Adaptive spectral shrinkage and empirical Bayes calibration
result Adapts to signal-to-noise ratio and shrinks superfluous components
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a mu…
This paper develops a new theory for ensemble learning beyond variance reduction.
problem Ensemble learning's effectiveness for stable estimators is not fully explained by variance reduction.
method Develops a general weighting theory for ensemble learning, formalizing ensembles as linear operators and introducing geometric and spectral constraints.
result Structured weights can outperform uniform averaging by reshaping approximation geometry and redistributing spectral complexity.
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rel…
We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two Alexander polynomials. From this point of view it is natural to s…
New method filters large networks from financial data to reveal key subnetworks.
problem Filtering large dimensional networks to isolate key constituents.
method Exploits spectral properties of high-dimensional data networks, tuning for sparsity and consistency.
result Shows method can interpolate between zero and maximal filtering, preserving spectral properties.
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…
Novel model captures high-dimensional copulas with spectral dynamics and regularization.
problem Modeling time-varying, asymmetric, tail-dependent copulas in high dimensions.
method Score-driven dynamics for eigenvalues, non-linear shrinkage for biases, parsimonious and scalable.
result Model outperforms recent alternatives in capturing co-movements and diversification potential.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
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.
A new method resolves permutation issues in shuffled linear regression for large-scale applications.
problem Estimating latent features through linear transformation with unknown permutations.
method Spectral matching method to align spectral components of measurement and feature covariances.
result Achieves accurate estimates in shuffled LS and LASSO settings with sufficient samples.
Improved portfolio optimization method reduces risk and improves performance.
problem Minimizing risk in large portfolios with limited data.
method Combines Tikhonov regularization and direct shrinkage of portfolio weights.
result Significantly reduces out-of-sample variance and Sharpe ratio compared to existing methods.
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.
PAS improves estimation of multiple means using ML predictions and shrinkage.
problem Improving statistical estimates with limited gold-standard data and noisy ML predictions.
method Prediction-Powered Adaptive Shrinkage (PAS) that combines PPI with empirical Bayes shrinkage.
result PAS adapts to the reliability of ML predictions and outperforms traditional methods in large-scale applications.
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the sh…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter ma…
Improved estimation of higher order integrals using shrinkage techniques.
problem Estimating higher order Bochner integrals in non-parametric settings.
method Shrinkage of U-statistic towards a target element, considering kernel degeneracy.
result Consistent shrinkage estimators with fast rates of convergence, even for non-degenerate kernels.
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.
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.
Improved stochastic gradient estimation for deep learning in high dimensions.
problem Inadmissibility of mini-batch gradients in high-dimensional settings.
method Stein-rule shrinkage applied to gradient computation.
result The proposed SR-Adam outperforms Adam in large-batch settings.
Stein shrinkage improves BN robustness against adversarial attacks.
problem Improving BN robustness against adversarial attacks.
method Applying Stein shrinkage to BN mean and variance estimates.
result Stein shrinkage outperforms vanilla BN in adversarial settings.
Guided adaptive shrinkage uses co-data to improve feature selection in genomic studies.
problem Feature selection challenges in high-dimensional genomics data, especially in clinical settings.
method Guided adaptive shrinkage methods that use co-data to adapt shrinkage parameters.
result Improves feature selection in genomic studies, demonstrated through comparisons and examples.
Proposes an efficient shrinkage path for ridge regression.
problem Ill-conditioned data in linear models.
method A new generalized ridge regression shrinkage path that minimizes MSE risk.
result The path is as short as possible while maintaining optimal trade-off.
This study evaluates shrinkage estimators for improving mean and covariance in portfolio optimization.
problem Estimation errors in expected returns and covariance matrix in mean-variance model.
method Examined five shrinkage estimators for expected returns and eleven for covariance matrix across six datasets.
result GMV model with Ledoit Wolf COV2 outperforms traditional methods in most scenarios.
We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider simultaneous estimation of all the parameters irrespective of their hidden states…
The paper explores how overfitting can lead to better predictions in high-dimensional data.
problem Understanding the behavior of linear models in high-dimensional settings with more predictors than observations.
method Analysis of ordinary least squares, penalized least squares, and spectral shrinkage estimates.
result The phenomenon of double descent, where model performance can improve with increasing model complexity.
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target. In a general framework, independent of a specific estimator, we extend the shrink…
GRASP simplifies Bayesian regression with grouped predictors using an adaptive NBP prior.
problem Regression with grouped predictors and adaptive shrinkage.
method Normal Beta Prime (NBP) prior with tunable hyperparameters for flexible sparsity control.
result Empirical validation of robust and versatile GRASP across various sparsity and signal-to-noise ratios.
High-dimensional shrinkage risk depends on the default prior for the common scale.
problem Choosing the default prior for the common scale in high-dimensional shrinkage.
method Using radial-power benchmark to compare variance-flat and standard deviation-flat priors.
result The standard deviation-flat prior has a one-unit asymptotic risk advantage near the origin.
Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.
problem Forecasting large covariance matrices of returns in finance.
method Decompose covariance matrix into firm-level factors and sectoral restrictions. Estimate using VHAR models with LASSO.
result Significantly improved forecasting precision compared to benchmarks.
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free es…
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of imag…
Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
problem Multicollinearity in Poisson regression models with experts.
method Ridge and Liu-type shrinkage methods.
result Shrinkage methods offer more reliable estimates for coefficients in multicollinearity.
Model for dynamic relational data with regime changes.
problem Handling abrupt changes in dynamic relational data.
method Factorized fusion shrinkage model with global-local shrinkage priors.
result Posterior distribution attains minimax optimal rate up to logarithmic factors.
Unified model combines shrinkage, views, and factor models for better portfolio selection.
problem Limitations of mean-variance analysis, estimation errors, and reliance on historical data.
method Bayesian approach integrating shrinkage estimation and Black-Litterman model with Fama-French factor models.
result The model outperforms simple and sample-based optimal portfolios in US equity market.
Non-linear shrinkage isn't optimal for portfolio optimization, especially when asset dependence is non-stationary.
problem Optimizing portfolios with non-stationary asset dependence structures.
method Derived and compared non-linear shrinkage with an optimal target for covariance matrix estimation.
result Non-linear shrinkage can be significantly improved for portfolio optimization.
We solve matrix denoising with both row and column correlations, setting limits and designing optimal methods.
problem Matrix denoising with doubly heteroscedastic noise (both row and column correlations).
method Established information-theoretic and algorithmic limits, designed a novel spectral estimator with optimality guarantees.
result The novel spectral estimator achieves positive correlation with the signal and Bayes-optimal error under one-sided heteroscedasticity.
Estimates growth loss in fund models and proposes a shrinkage method.
problem Estimating growth loss in fund models under frequentist and Bayesian estimation.
method Proposes a shrinkage method to target maximal growth with minimal deviation.
result Empirical evidence shows shrinkage gives a stable estimate closer to growth potential.
New shrinkage estimator for GMV portfolio reduces risk in high-dimensional asset settings.
problem Estimating the global minimum variance portfolio in high-dimensional settings with limited data.
method Dynamic shrinkage of the GMV portfolio using previous data as a target.
result The new estimator outperforms traditional methods in high-dimensional asset settings.
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Optimizes high-dimensional portfolios using joint shrinkage.
problem Optimizing portfolios with many assets where classical methods fail.
method Regression-based joint shrinkage method for estimating partial correlations.
result Superior performance in variance, weight, and risk estimation compared to other methods.
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, resp…