We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form…
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.
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.
WCPS extends CPS to handle covariate shifts, providing probabilistically calibrated predictions.
problem Applying CPS to scenarios with covariate shifts.
method WCPS uses likelihood ratios between training and testing covariate distributions.
result WCPS are probabilistically calibrated under covariate shift.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
problem Jointly estimate multiple related zero-mean Gaussian distributions.
method Laplacian regularized stratified model fitting with hyper-parameters to encourage covariance closeness.
result The method performs well, especially in low data regimes, as demonstrated in finance, radar, and weather.
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.
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to remove the bias between training and testing distributions using importance weigh…
Efficiently estimates covariance matrix for elliptical distributions under strong contamination.
problem Robust estimation of covariance matrix in the presence of adversarial corruptions.
method Proposes an algorithm that uses spatial sign of elliptical distributions and spectral covariance filtering.
result Achieves nearly optimal error guarantee for various elliptical distributions.
Algorithm calibrates predictions for covariate shift using domain adaptation.
problem Uncertainty estimates overestimate certainty when real-world data differs from training data.
method Uses importance weighting and learns a feature map to equalize distributions.
result Outperforms existing approaches in calibrated prediction when covariate shift occurs.
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.
Meta-learning improves with explicit modeling of task covariate distributions.
problem Ignoring the relationship between task covariates and conditional distributions limits meta-learning performance.
method Introducing a hierarchical Bayesian model that leverages samples from the marginal task covariates to better infer optimal parameters.
result Our method outperforms initialization-based meta-learning on popular classification benchmarks.
Bayesian framework improves uncertainty estimates under covariate shifts.
problem Neural networks' unreliable uncertainty estimates under covariate shifts.
method Adaptive prior conditioned on training and new covariates, amortized variational inference.
result Significantly improved uncertainty estimates under distribution shifts.
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 paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.
problem Understanding the influence of Gaussian kernel parameters on posterior covariance in Gaussian processes.
method Geometric analysis and a posteriori error estimation techniques from adaptive finite element methods.
result The bandwidth parameter and spatial distribution of observations significantly influence posterior covariance and its matrix.
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.
The paper addresses the reliability of conformal prediction under covariate shift.
problem Ensuring reliable prediction sets under covariate shift.
method Derives upper bounds on training-conditional coverage.
result Offers PAC guarantees for conformal prediction methods.
New similarity measure for covariate shift improves nonparametric regression rates.
problem Improving nonparametric regression under covariate shift.
method Introducing a new similarity measure based on probability ratios.
result Shows a sharper rate of convergence compared to transfer exponent.
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.
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.
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.
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.
FIRE method improves model performance in federated learning by penalizing fragmentation-induced covariate shifts.
problem Performance degradation in federated learning due to data fragmentation and covariate shift.
method FIRE method accumulates fragmentation-induced covariate shift divergences via approximate Fisher information and uses it as a per-fragment loss penalty.
result FIRE outperforms importance weighting and federated learning benchmarks by up to 5.3% on shifted validation sets.
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
This paper examines how adversarial perturbations affect model performance and equilibrium learning.
problem Adversarial perturbations and covariate shifts impact model performance and equilibrium learning.
method Characterizes the extrapolation region in regression and classification, analyzes dynamics of adversarial learning games.
result Establishes two directional convergence results: a blessing in regression and a curse in classification.
New methods estimate covariance for matrix data without assuming fixed size or specific distributions.
problem Estimating covariance for high-dimensional matrix data without distributional assumptions.
method Unified framework for bandable covariance estimation with rank one approximation, robust to heavy-tailed data.
result Proposed estimators are rate-optimal and perform well in simulations and real applications.
Unified method for inference on partially identified causal effects using covariates.
problem Partial identification of causal effects due to unobserved joint potential outcomes.
method Model-agnostic approach using duality theory for optimal transport problems.
result Uniformly valid inference for a wide class of estimands, even with inaccurate nuisance parameter estimates.
Bayesian approach models match and non-match score distributions over continuous covariates.
problem Complex evaluation of model performance over continuous covariates in biometric verification.
method Generative model of score distributions, mixture models, local basis functions, Bayesian inference.
result Accurate and effective method for studying model performance over continuous covariates.
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 …
A regression algorithm uses Green's function and covariance matrix for predictive distributions.
problem Regression and uncertainty quantification for machine learning.
method Green's function theory, Bayesian approach, covariance matrix of normalized Green's function.
result The covariance matrix provides predictive distributions with mean and confidence intervals.
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different machines. We address communication efficiency by proposing a method where, in a si…
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
Paper solves a key problem in learning from high-dimensional covariance matrices.
problem Computing normalizing factors for Riemannian Gaussian distributions on high-dimensional covariance matrices.
method Equivalence with random matrix theory and log-normal matrix ensembles to approximate normalizing factors.
result Efficient approximation of normalizing factors with decreasing error as dimension increases.
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.
New method estimates covariance matrices without restrictive assumptions.
problem Estimating high-dimensional covariance matrices under restrictive assumptions.
method Distributionally robust covariance estimation problems with mild conditions.
result Robust estimators are efficient, consistent, and perform well.
Paper addresses off-policy evaluation and learning with covariate shift.
problem Evaluating and training a new policy using historical data with a covariate shift.
method Derives efficiency bounds and proposes doubly robust estimators for OPE and OPL under covariate shift.
result Proposes estimators for off-policy evaluation and learning under covariate shift.
Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.
problem Estimating sparse linear regression coefficients with heavy-tailed and outlier-contaminated data.
method Efficient computation of estimators with sharp error bounds.
result Sharp error bounds for efficient estimators.
Study optimal ridge regularization for out-of-distribution prediction.
problem Optimal ridge regularization for predicting out-of-distribution data.
method Established conditions for optimal regularization under covariate and regression shifts, proving monotonic risk in data aspect ratio.
result Negative regularization can be optimal under shifts, even with isotropic or underparameterized training features.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance …
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.
We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order d/n in dimension d with n samples. Here, we study the minimax expected excess risk over the full linear class, depending on the dist…
Paper introduces a novel measure to analyze excess error in classification under covariate shift.
problem Analyzing excess error in classification under covariate shift.
method Utilizes vicinity information to characterize excess error.
result Faster or competitive convergence rates compared to previous techniques.
Improves regression models' performance on covariate shift.
problem Out-of-distribution generalization for regression.
method Spectrally adapting the weights of a pre-trained neural regression model.
result Spectral adaptation improves out-of-distribution performance.
RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.
New algorithm mitigates misspecification amplification in regression models with covariate shift.
problem Distribution shift and model misspecification in regression models.
method Developed a new algorithm inspired by robust optimization to avoid misspecification amplification.
result No misspecification amplification while still achieving optimal statistical rates.
Bayesian PROCOVA uses AI to adjust for covariates in RCTs.
problem Unbiased and precise treatment effect inferences from RCTs.
method Generative AI constructs digital twins for covariate adjustment, using an additive mixture prior.
result Efficiency gains in smaller RCTs compared to frequentist methods.
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme dimension reduction, i.e. to very low dimensions, in improving the performance of imp…