Unified derivation of high-dimensional linear models using stochastic gradient descent.
problem Performance analysis of high-dimensional linear models trained with stochastic gradient descent.
method Derivation of a deterministic equivalence for the two-point function of a random matrix resolvent.
result Unified understanding of model performance including previously known and novel results.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
Paper introduces semi-supervised linear extremile regression for high-dimensional data.
problem Challenges in high-dimensional extremile regression due to data sparsity and overfitting.
method Proposes semi-supervised learning for linear extremile regression, achieving n \sqrt{n} n -consistency. result Demonstrates improved estimation efficiency and performance in high-dimensional settings.
Nested model averaging improves high-dimensional linear regression performance.
problem High-dimensional linear regression with predictor ordering impact.
method Combining model averaging with regularized estimators on the solution path.
result Nested model averaging with lasso and SLOPE outperforms competing methods.
Study shows double descent curve in high-dimensional linear regression with random projections.
problem Understanding the generalization performance in high-dimensional settings with random projections.
method Fixed prediction problem, ridge regression estimator, minimum norm least-squares fit, random matrix theory, asymptotic equivalents.
result Exhibit a double descent curve for high-dimensional linear regression with random projections.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
New methods combine low and high-fidelity data for accurate surrogate modeling.
problem Challenges in surrogate modeling for high-dimensional outputs with limited training data.
method Projection-based multifidelity linear regression methods integrating low-fidelity and high-fidelity data.
result Multifidelity methods achieve up to 12% improvement in median accuracy compared to single-fidelity methods.
A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.
problem Statistical inference for low-dimensional parameters in high-dimensional linear regression models.
method Mean-field variational Bayes approach, focusing on nuisance parameters and conditional distributions.
result Competitive numerical performance and theoretical guarantees for estimation and uncertainty quantification.
Lecture notes on advanced linear regression methods.
problem Understanding the properties of linear regression estimators in high dimensions.
method Proposition-proof exploration of least squares, ridgeless, ridge, and lasso estimators.
result Detailed analysis of the existence, uniqueness, relations, computation, and non-asymptotic properties of these estimators.
The paper tackles high-dimensional mixed linear regression with unknown parameters and proposes methods for estimation, confidence intervals, and hypothesis testing.
problem High-dimensional mixed linear regression with unknown parameters and covariance structure.
method Iterative high-dimensional EM algorithm for estimating regression vectors, debiased estimators for individual coordinates, and large-scale multiple testing procedure.
result Asymptotic normality of debiased estimators and FDR control for hypothesis testing.
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
PROBE algorithm efficiently solves sparse high-dimensional linear regression.
problem Sparse high-dimensional linear regression models with complex parameter spaces.
method Partitioned empirical Bayes ECM algorithm for computationally efficient MAP estimation.
result PROBE algorithm provides robust and efficient coordinate-wise optimization.
New method bounds high-dimensional regression without estimating design covariance.
problem High-dimensional linear regression with random design.
method Error-in-operator approach that incorporates design covariance into empirical risk minimization.
result Dimension-free bounds on excess prediction risk derived.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
Paper addresses high-dimensional linear regression with missing data, proposing efficient and nearly unbiased estimators.
problem High-dimensional linear regression with blockwise missing covariates and partially observed responses.
method Proposes a computationally efficient estimator and nearly unbiased debiased estimators using blockwise imputation and estimating equations.
result Asymptotically valid confidence intervals and statistical tests constructed based on debiased estimators.
Estimates CATEs using high-dimensional linear regression models.
problem Estimating individualized causal effects (CATEs) in two treatments.
method Proposes a Lasso regression method for consistently estimating CATEs under high-dimensional and non-sparse parameters, leveraging the assumption of implicit sparsity.
result The proposed method is consistent for estimating CATEs.
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-…
New CLT for SGD in high-dimensional regression provides online inference.
problem Quantifying uncertainty in SGD for high-dimensional regression.
method Established a high-dimensional CLT for online SGD iterates.
result Developed an online approach for estimating variance in CLT.
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
Study optimizes linear regression analysis for high-dimensional settings.
problem Understanding high-dimensional linear regression with interpolation and regularization.
method Localized uniform convergence analysis of optimistic rates for linear regression.
result Recover guarantees for ridge and LASSO regression under random designs.
Sequential coordinate ascent is more robust in high-dimensional linear regression.
problem Behavior difference between sequential and parallel coordinate ascent in variational inference.
method Comparison of sequential and parallel coordinate ascent algorithms in high-dimensional linear regression.
result Sequential algorithm converges under more relaxed conditions than parallel algorithm.
New AMP algorithm detects change points in high-dimensional GLMs.
problem Detecting change points in high-dimensional GLMs.
method Approximate Message Passing (AMP) algorithm for estimating signals and change points.
result Characterization of AMP algorithm's performance in high-dimensional limit.
Simple linear models outperform complex BO methods in high dimensions.
problem Overcoming the curse of dimensionality in Bayesian optimization.
method Bayesian linear regression with linear kernels, applied to high-dimensional search spaces.
result Simple linear models match or outperform state-of-the-art BO methods in high-dimensional tasks.
SVM and linear regression models coincide in high dimensions.
problem Understanding the connection between SVM and linear regression in high-dimensional data.
method Analyzing feature models and proving lower bounds on dimensionality.
result A sharp phase transition in Gaussian feature models, with support vector proliferation occurring only in very high dimensions.
Paper tackles distributed quantile regression with improved efficiency and support recovery.
problem Challenges in distributed estimation and support recovery for high-dimensional linear quantile regression.
method Transformed quantile regression into least-squares optimization, applied double-smoothing approach, developed efficient algorithm.
result Achieved near-oracle convergence rate and high support recovery accuracy.
We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most i…
Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
The paper analyzes high-dimensional linear regression using parametric empirical Bayes methods.
problem Estimation of i.i.d. priors in high-dimensional Bayesian linear regression with random design.
method Parametric empirical Bayes estimation, variational lower bound maximization, phase transition analysis.
result The vEB estimator is information theoretically optimal up to p = o ( n 2 / 3 ) p=o(n^{2/3}) p = o ( n 2/3 ) but sub-optimal in higher dimensions. The paper improves high-dimensional linear regression prediction and estimation using auxiliary samples.
problem Estimating and predicting high-dimensional linear regression models with auxiliary samples.
method Proposes Trans-Lasso for data-driven transfer learning, establishing optimality for prediction and estimation.
result Knowledge from auxiliary samples can improve learning performance in target problems.
Study of Bayes optimal learning in high-dimensional linear regression with network side information.
problem Bayes optimal learning in high-dimensional linear regression with network side information.
method Introduce a Reg-Graph model and an iterative AMP algorithm for Bayes optimality under general conditions.
result Characterization of the limiting mutual information between latent signal and data observed.
In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior…
Enhances kernel regression with network data for better predictions.
problem Improving predictive power in high-dimensional data.
method Combines kernel regression with network cohesion data to model nonlinearities.
result Significantly better predictive performances in high-dimensional data.
New approach quantifies overfitting in high-dimensional regression.
problem Quantifying and avoiding overfitting in large neural networks.
method Information bottleneck theory to minimize residual information while maximizing relevant bits.
result Characterized the relative information efficiency of randomized regression compared to optimal algorithms.
This work studies scaling laws for low-precision training in high-dimensional linear regression.
problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.
A neural network model tackles high-dimensional data with latent structures.
problem Modeling high-dimensional data with latent low-dimensional structures.
method Integrates PCA and Soft PCA layers into neural network architecture for factor modeling and non-linear transformations.
result Demonstrates improved performance in forecasting and nowcasting with real-world data.
Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.
problem Computational challenges in high-dimensional ℓ 1 \ell_1 ℓ 1 penalized quantile regression. method Pathwise coordinate descent algorithm to solve exact coordinatewise minimum of the nonsmooth loss function.
result Algorithm runs faster than existing alternatives and maintains estimation accuracy.
New algorithm for robust high-dimensional linear regression is both fast and statistically optimal.
problem Challenges in high-dimensional linear regression under heavy-tailed noise or outliers.
method Projected sub-gradient descent algorithm for sparse and low-rank regression problems.
result Algorithm achieves linear convergence and statistical optimality under various noise conditions.
New method improves regression estimates, reducing bias.
problem Omitted variable bias in high-dimensional linear regression.
method Post-Double-Autometrics, an alternative to Post-Double-Lasso.
result Post-Double-Autometrics outperforms Post-Double-Lasso.
TSRGA scales multivariate linear regression for feature-distributed data.
problem Multivariate linear regression for feature-distributed data with high dimensions and many computing nodes.
method Two-stage relaxed greedy algorithm (TSRGA) for multivariate linear regression.
result TSRGA is highly scalable and can yield low-rank coefficient estimates.
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that…
Transfer learning improves MNI's performance in high-dimensional linear regression.
problem Improving model performance in high-dimensional linear regression with diverse data.
method Proposes a Transfer MNI approach, analyzing its excess risk and conditions for outperformance.
result Identifies free-lunch covariate shift regimes where knowledge transfer benefits.
Study quantization effects on high-dimensional linear regression learning.
problem Understanding quantization's impact on learning high-dimensional linear regression models.
method Analyzes stochastic gradient descent for high-dimensional linear regression under various quantization targets.
result Establishes precise bounds on excess risk for different quantization schemes.
New method predicts aphasia severity with narrower uncertainty intervals.
problem Predicting aphasia severity in stroke patients using neuroimages.
method Sparse heteroscedastic Bayesian high-dimensional regression with H-PROBE algorithm.
result H-PROBE provides narrower prediction intervals for aphasia severity.
The paper analyzes how generated data improves adversarial training in high-dimensional regression.
problem Improving adversarial training in high-dimensional regression.
method Theoretical analysis of a two-stage training approach with generated data and pseudo-labels.
result Two-stage adversarial training achieves better performance than ridgeless training in high-dimensional linear regression.
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile …
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber M M M -estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, t…
Study ridge regression for non-identically distributed data with varying variances.
problem Investigate high-dimensional regression with non-identical data variance.
method Propose a random effect model and use tools from random matrix theory.
result Highlight the double descent phenomenon in high-dimensional regression for certain variance profiles.