Global covariance pooling improves deep CNNs' representation and generalization.
problem Capturing richer statistics of deep features for better representation and generalization.
method Integrates global covariance pooling into deep CNNs, addressing challenges with robust covariance estimation and geometry exploitation.
result Proposes MPN-COV Pooling and a Gaussian embedding network, achieving state-of-the-art performance.
This paper analyzes generalization for linear models with spiked covariance structures.
problem Understanding the generalization performance of linear models with spiked covariance structures.
method Derives the generalization error for two simple models with spiked covariances using random matrix theory.
result The eigenvector and eigenvalue corresponding to the spike significantly influence the generalization error.
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.
The paper proves a new method to improve generalization in covariate-shift scenarios.
problem Improving performance on test distributions that differ from training distributions.
method Independence-driven importance weighting algorithms for feature selection.
result Theoretical proof that these algorithms can identify optimal variables for covariate-shift generalization.
New covariance function improves climate model accuracy.
problem Non-stationary and non-uniform spatial data in climate modeling.
method Intrinsic non-stationary covariance function for Gaussian process regression.
result Improved regression estimates for relative sea level changes.
New method predicts covariate shift with various losses and feature views.
problem Covariate shift prediction with poor performance guarantees and high variance.
method Robustly minimize various loss functions and shape influence by feature views.
result Improved robustness and applicability to more task scenarios.
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.
Predict covariance from features using convex optimization.
problem Predicting the covariance of a Gaussian vector from another feature vector.
method A generalized linear model with convex optimization for fitting parameters.
result Predicted covariance matrices are symmetric positive definite.
New method recovers graph structure from covariance queries efficiently.
problem Recovering graph structure from covariance matrices in high dimensions.
method Proposes a new input model allowing covariance queries and proves support recovery for tree-like graphs.
result Support of the inverse covariance matrix can be recovered efficiently with low query and computational complexity.
Estimates covariance matrix from low-dimensional compressive measurements.
problem Estimating covariance matrix from limited data.
method Unbiased estimator using i.i.d. zero-mean entries with finite moments.
result Accurate estimation of covariance matrix on real-world data.
The paper addresses the selection of synthetic data for improving classifier performance, focusing on the role of covariance shift.
problem The effectiveness of synthetic data in improving classifier performance is questioned, and the specific properties affecting this performance are unclear.
method The paper uses high-dimensional regression to analyze synthetic data selection, focusing on the covariance shift between synthetic and target distributions.
result The covariance shift between synthetic and target distributions affects the generalization error of classifiers, but the mean shift does not.
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…
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. 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.
A new covariance estimator reduces dimensionality and improves portfolio forecasting.
problem Estimating high-dimensional covariance matrices with weak factors.
method Sparse Approximate Factor (SAF) model with l 1 l_1 l 1 -regularization. result SAF estimator outperforms other methods in portfolio forecasting.
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.
New approach for semi-supervised learning under covariate shifts.
problem Semi-supervised learning under covariate shifts where labeled and unlabeled data distributions differ.
method Information-theoretical approach, addressing covariate shifts.
result Improved performance compared to previous methods.
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and…
Study semi-supervised learning with noisy proxy covariates, deriving bounds and showing gains.
problem Learning from noisy proxy covariates with scarce labels.
method Two-stage estimator learning kernel eigenfeatures from all proxy covariates and fitting a ridge predictor on labeled data.
result Finite sample bounds show fast labeled sample rates and consistent gains over supervised and semi-supervised baselines.
Constructs covariant derivatives for Ehresmann connections.
problem Developing a method for covariant derivatives in fibre bundles.
method Introducing a vertical endomorphism to construct covariant derivatives on vertical and horizontal distributions.
result Covariant derivatives can be constructed separately on vertical and horizontal distributions and then glued together.
Enhanced Transformer models predict ETF portfolio performance by optimizing covariance and semi-covariance matrices.
problem Static covariance estimates fail to capture dynamic market fluctuations and non-linear correlations.
method Transformer-based models for real-time covariance and semi-covariance predictions.
result Portfolios optimized with semi-covariance matrix outperform those with standard covariance matrix, especially in volatile conditions.
Covariance graphical lasso applies a lasso penalty on the elements of the covariance matrix. This method is useful because it not only produces sparse estimation of covariance matrix but also discovers marginal independence structures by generating zeros in the covariance matrix. We propose and explore two new algorith…
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.
New methods estimate survival functions with time-varying covariates.
problem Estimating survival functions with time-varying covariates.
method Generalized conditional inference and relative risk forests, adapted transformation forest.
result Proposed methods outperform traditional models in estimating survival functions.
The paper analyzes covariance of embedded manifolds to extract curvature information.
problem Understanding curvature of submanifolds embedded in higher-dimensional spaces.
method Covariance analysis of point sets on embedded Riemannian manifolds, focusing on volume and curvature.
result Eigenvalue decompositions of covariance matrices have asymptotic expansions containing curvature information.
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.
The paper argues for using Neyman orthogonal score for balancing in debiased machine learning.
problem Debiased machine learning requires a proper approach to balance covariates.
method The paper advocates for using Riesz regression with basis functions of X for balancing.
result Covariate balancing is only valid when the score-relevant regression error is a function of covariates alone.
Dynamic pricing algorithms can work with covariates without i.i.d. assumptions.
problem Dynamic pricing with covariates under a generalized linear demand model.
method UCB and Thompson sampling-based pricing algorithms.
result Achieves an O ( d T log T ) O(d\sqrt{T}\log T) O ( d T log T ) regret upper bound without i.i.d. covariates assumption. Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
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.
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.
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…
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.
Diagonal transformations preserve independence structures in non-Gaussian distributions.
problem Preserving independence structures in non-Gaussian distributions.
method Diagonal nonlinear transformations of multivariate normal variables.
result Independence structures are preserved in non-Gaussian distributions under diagonal transformations.
Optimizes treatment allocation using covariates for better outcomes.
problem Improving treatment allocation in multi-armed bandit problems.
method Maximizes a functional of the conditional potential outcome distribution.
result Developed expected regret lower bounds and near minimax optimal policy.
We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors.
Homotopy equivalence between formalities with different covariant derivatives.
problem Formality of Dolgushev depends on covariant derivative choice.
method Proved homotopy equivalence of L ∞ L_\infty L ∞ -morphisms twisted by gauge equivalent elements. result Globalized formalities with different covariant derivatives are homotopic.
We calculate eigenvector overlaps between intersecting time periods of covariance matrices.
problem Analyzing overlapping time periods in covariance matrices.
method Girko linearisation and extended local laws.
result Computed eigenvector overlaps for intersecting time intervals.
Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
New method estimates large covariance matrices using nonconvex penalties.
problem Estimating large covariance matrices in high-dimensional data.
method Developed a first-order algorithm using generalized nonconvex penalties.
result Positive-definite covariance estimators using nonconvex penalties.
The paper updates Bayesian CMA-ES with normal Wishart and proves lower expected covariance.
problem Improving the Bayesian CMA-ES algorithm with normal Wishart prior.
method Revisits Bayesian CMA-ES, proves lower expected covariance in normal Wishart, and presents a generalized model.
result Proves that the expected covariance is lower in the normal Wishart prior model due to convexity of the inverse.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
The study improves generalization in large-batch training by adding structured covariance noise to gradients.
problem Improving generalization in large-batch training while maintaining optimal convergence.
method Adding covariance noise to the gradients to improve generalization performance.
result The method improves generalization performance without degrading optimization performance and training duration.
Semi-generative model learns causes and effects for covariate-shift adaptation.
problem Covariate shift adaptation with unlabelled data and causal features.
method Combines semi-supervised learning with causal features X C X_C X C and X E X_E X E . result Significant improvements in classification over baselines.
A new mathematical approach to general covariance using stacks and Lie algebras.
problem Understanding general covariance in curved spacetime field theories.
method Using stacks and groupoids to study the quotient of metrics modulo diffeomorphism, and analyzing the tangent complex and Lie algebra actions.
result Recovering a novel expression for the stress-energy tensor in scalar field theories.
Researchers create a family of conformally covariant operators.
problem Developing a comprehensive set of conformally covariant operators.
method Constructing a family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space.
result Symmetrization of ambient operators is formally self-adjoint.
Paper tackles backwards-compatible data adaptation for confounded covariate and label shifts.
problem Adapt covariates to predict labels confounded with covariate shifts.
method Proposes confounded shift framework based on minimizing divergence between source and target conditional distributions, conditioning on confounders.
result Demonstrates approach on synthetic and real datasets, achieving backwards-compatible data adaptation.