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.
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 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.
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…
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.
Noise in linear networks minimizes sharpness and leads to shrinkage-thresholding.
problem Minimizing sharpness in diagonal linear networks.
method Stochastic sharpness-aware minimization (SAM) with isotropic noise.
result Noise forces shrinkage-thresholding of true parameters.
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.
New insights into contrastive learning reveal how projectors affect downstream performance.
problem Understanding how projectors in contrastive learning impact downstream linear classification accuracy.
method Identified and modeled two effects: expansion and shrinkage induced by contrastive loss.
result Linear projectors operating in the shrinkage regime hinder downstream classification accuracy.
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.
A new method for linear regression using feature graphs and hierarchical shrinkage.
problem Estimating robust parameters for linear regression models.
method Hierarchical Feature Regression (HFR) estimator that constructs a supervised feature graph to shrink parameters towards group targets.
result Demonstrates good predictive accuracy and versatility compared to other regularization techniques.
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.
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
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables p→∞ and the sample size n→∞ so that p/n→c∈(0,+∞). The precision matrix is estimated directly, wit…
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distanc…
New estimators improve sparse semiparametric additive modeling.
problem Sparse semiparametric additive modeling with structured sparsity.
method Combines group subset selection with shrinkage for nonconvex optimization.
result New estimators outperform alternatives in synthetic and real-world data.
This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables X,Y are independent or not, a question that comes up in many fields like causality and neuroscience. While quantities like correlation o…
This paper considers improved forecasting in possibly nonlinear dynamic settings, with high-dimension predictors ("big data" environments). To overcome the curse of dimensionality and manage data and model complexity, we examine shrinkage estimation of a back-propagation algorithm of a deep neural net with skip-layer c…
New damping technique improves deep learning models by reducing noise in flat directions.
problem Improving generalization in deep learning models by reducing estimation noise in flat directions.
method Developed a novel random matrix theory based damping learner to reduce the shrinkage coefficient and improve generalization.
result Significant generalization improvements in logistic regression and deep neural networks experiments.
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.
Improved DSSMs for easier interpretable latent variables.
problem Complex and hard-to-interpret latent variables in DSSMs.
method Simplified predictive decoder and shrinkage priors.
result Interpretable latent variables improve forecasting performance.
Improved classification model for high-cardinality categorical predictors.
problem Handling high-cardinality categorical predictors and non-linear data.
method Data-driven binning of spline functions and shrinkage estimators.
result Improved classification precision with interpretable predictors.
A VB method for high-dimensional regression with student-t priors achieves nearly optimal performance and computational efficiency.
problem High-dimensional linear model inferences with heavy-tailed shrinkage priors.
method Variational Bayesian (VB) procedure for high-dimensional linear models with student-t priors.
result The VB method achieves nearly optimal contraction rate and computational efficiency, outperforming MCMC methods.
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it al…
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.
Inflating the minimum norm interpolator improves linear regression generalization error.
problem Highly anisotropic covariances and diverging d/n in linear regression. method Inflating the minimum ℓ2 norm interpolator by a constant greater than one. result Inflating the minimum norm interpolator improves generalization error.
Nash integrates covariate-specific side info into sparse regression via neural networks.
problem Sparse linear regression struggles with covariates exhibiting structure or coming from heterogeneous sources.
method Neural Adaptive Shrinkage (Nash) framework that integrates side information into sparse regression via neural networks. Uses split variational empirical Bayes algorithm.
result Nash improves accuracy and adaptability over existing methods in real data experiments.
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…
Flexible empirical Bayes for large-scale multiple linear regression.
problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.
In this article we present an approach that enables joint wind speed and wind power forecasts for a wind park. We combine a multivariate seasonal time varying threshold autoregressive moving average (TVARMA) model with a power threshold generalized autoregressive conditional heteroscedastic (power-TGARCH) model. The mo…
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…
Estimates dependent parameters using Markovian dependence with shrinkage.
problem Estimating dependent parameters from a hidden Markov model.
method Developed a novel non-parametric shrinkage algorithm combining Tweedie-based ideas and efficient state estimation.
result Superior performance compared to non-shrinkage methods in hidden Markov models.
Bayesian method selects subsets for LMMs with structured dependence.
problem Subset selection challenge in LMMs with structured dependence.
method Bayesian decision analysis with Mahalanobis loss function.
result Optimal linear coefficients for subsets and cardinality constraints.
In this paper we derive the optimal linear shrinkage estimator for the high-dimensional mean vector using random matrix theory. The results are obtained under the assumption that both the dimension p and the sample size n tend to infinity in such a way that p/n→c∈(0,∞). Under weak conditions imposed on…
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.
Since the advent of the horseshoe priors for regularization, global-local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high-dimensional regression and classification problems. They have achieved remarkable success in computation, …
We revisit the problem of feature selection in linear discriminant analysis (LDA), that is, when features are correlated. First, we introduce a pooled centroids formulation of the multiclass LDA predictor function, in which the relative weights of Mahalanobis-transformed predictors are given by correlation-adjusted t…
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.
Flexible co-data learning improves clinical prediction models.
problem High-dimensional clinical data challenges prediction accuracy.
method Combining domain knowledge and external studies to estimate adaptive multi-group ridge penalties.
result Improves prediction performance and variable selection stability.
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.
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.
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called l0 norm. In this paper we develop a Momentumized Iterative Shrinkage Th…
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.
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.
BaGGLS models biological interactions using Bayesian shrinkage for interpretability.
problem Interpreting complex interactions in high-dimensional biological data.
method Bayesian group global-local shrinkage prior with variational approximation.
result BaGGLS outperforms other methods in interaction detection and scalability.
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…