Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
A novel Bayesian framework for private linear regression with MCMC.
problem Private linear regression in a distributed setting.
method Generative statistical model, MCMC algorithms, fast Bayesian estimation.
result The proposed methods provide well-rounded estimation and prediction.
Study robust linear regression without distributional assumptions for heavy-tailed responses.
problem Linear regression with heavy-tailed responses and no distributional assumptions.
method Combining truncated least squares, median-of-means, and aggregation theory to construct a non-linear estimator.
result Achieves excess risk of order d / n d/n d / n with optimal sub-exponential tail. 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.
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.
Two EM algorithms estimate prior distributions in mixture of linear regressions.
problem Estimating prior distributions in mixture of linear regressions.
method Two EM algorithms: one for continuous priors, one for discrete priors.
result Both algorithms accurately estimate prior distributions and the number of clusters.
Local SGD proves efficient in overparameterized linear regression.
problem Efficiently learning overparameterized linear models in distributed settings.
method Distributed SGD (DSGD) with overparameterized models.
result Excess risk of SGD is smaller than ridge regression in the same sample complexity.
Neural linear model performs well on simple regression tasks but requires tuning.
problem Characterizing the neural linear model's performance on simple regression tasks.
method Characterized the neural linear model on UCI and gap datasets.
result The neural linear model shows good performance but requires good hyperparameter tuning.
Analyzes generalization error in distributed linear regression.
problem Understanding generalization performance in distributed learning.
method Analytical characterization of generalization error in linear regression with distributed learning.
result Generalization error increases dramatically when nodes estimate close to the number of observations.
Paper studies IPG method's robustness in noisy distributed linear regression.
problem Distributed linear regression with noise.
method Iteratively Pre-conditioned Gradient-descent (IPG) method.
result IPG method's robustness against noise compared favorably to state-of-the-art algorithms.
Study improves generalization bounds for linear regression across tasks.
problem Improving generalization in high-dimensional regression problems.
method Distribution-dependent bounds on generalization error for L1, L2, and elastic net regularization.
result Generalization bounds improve with data distribution niceness and do not degrade with feature dimension.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
Wasserstein framework solves mixed linear regression problems.
problem Mixed linear regression with multi-modal distributions.
method Wasserstein distance minimization for nonconvex-concave minimax optimization.
result WMLR achieves global convergence and generalization guarantees for two linear models.
Distributed sensors compress and send features to a fusion center for linear regression.
problem Efficiently compress and transmit features from distributed sensors to a fusion center under varying communication constraints.
method Designs a distributed and adaptive feature compression scheme using optimal quantizers and simple adaptive strategies.
result Demonstrates improved inference performance through simulated experiments.
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
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.
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.
Study reveals how manifold geometry impacts linear regression solutions.
problem Impact of manifold geometry on linear regression solutions.
method Linear regression applied to manifold-structured data, focusing on extrinsic geometry.
result Linear regression does not have a unique solution on flat manifolds.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
The paper tackles domain generalization using functional regression.
problem Learning a model that generalizes well across different source distributions.
method Functional regression approach to learn a linear operator between marginal and conditional distributions.
result The proposed algorithm achieves finite sample error bounds for the idealized risk.
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.
Study on distributed linear regression performance, focusing on generalization error.
problem Performance of distributed learning in large-scale linear regression.
method Statistical learning approach, focusing on generalization error.
result Generalization error of distributed solution can be higher than centralized solution.
The paper examines efficient algorithms for linear regression over resource-limited networks.
problem Efficient communication in distributed learning over resource-limited networks.
method Developed algorithms for communication-efficient learning of linear regression tasks.
result The algorithms enable a tradeoff between communication and learning with theoretical performance guarantees.
New method for private linear regression under privacy constraints, achieving optimal rates.
problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear reg…
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.
problem Outliers and heavy-tailed noise in linear regression coefficients.
method Sharp concentration inequalities and generic chaining.
result Sharper error bounds under weaker assumptions.
Locally adaptive interpretable regression improves linear regression's predictability.
problem Linear regression's predictability is limited; it lacks adaptability.
method Locally adaptive interpretable regression (LoAIR) uses neural networks to predict percentile of a Gaussian distribution for regression coefficients.
result LoAIR achieves comparable or better predictive performance than state-of-the-art baselines.
A new type of distributional regression tree uses soft split rules for better predictive performance.
problem Estimating complete conditional distributions in regression.
method Distributional adaptive soft regression trees using multivariate soft split rules.
result The method outperforms various benchmark methods, especially in complex non-linear interactions.
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
Task shift from classification to regression is possible in overparameterized linear models with limited additional data.
problem Transferability of latent knowledge from classification to regression in overparameterized linear models.
method Investigation of task shift in overparameterized linear regression, zero-shot and few-shot cases, with a focus on minimum-norm interpolation.
result Minimum-norm interpolators can transfer latent knowledge from classification to regression with limited additional data.
We detail distributed algorithms for scalable, secure multiparty linear regression and feature selection at essentially the same speed as plaintext regression. While the core geometric ideas are simple, the recognition of their broad utility when combined is novel. Our scheme opens the door to efficient and secure geno…
Paper tackles distributed linear regression with compositional covariates.
problem Solving distributed statistical methodology and computing for massive compositional data.
method Proposes two distributed optimization techniques based on ADMM and CDMM for solving constrained convex optimization problems.
result Established convergence theories for the proposed algorithms under regularity conditions.
This paper considers the problem of Byzantine fault tolerance in distributed linear regression in a multi-agent system. However, the proposed algorithms are given for a more general class of distributed optimization problems, of which distributed linear regression is a special case. The system comprises of a server and…
Distributed-OMP recovers sparse vectors with low communication costs.
problem High-dimensional sparse linear regression with limited computation and communication.
method Distributed orthogonal matching pursuit (OMP) scheme.
result Support of the regression vector can be recovered with linear communication per machine and logarithmic in dimension.
Improved linear regression for diverse data batches.
problem Learning from multiple heterogeneous data sources.
method Gradient-based algorithm for different input distributions.
result Significant reduction in the number of required batches and sample size.
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.
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.
Study improves error bounds for sparse regression with heavy-tailed covariates.
problem Estimating sparse coefficients in linear regression with heavy-tailed covariates.
method Employed an ℓ 1 \ell_1 ℓ 1 -penalized Huber regression method. result Error bound identical to Gaussian case for L L L -subexponential covariates. 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 …
Derives TAP approximation for Bayesian linear regression.
problem Log-normalizing constant of posterior distribution in high-dimensional linear regression.
method Variational representation and Thouless-Anderson-Palmer approximation.
result Proves TAP approximation for spherical prior in proportional asymptotic regime.
CNR uses convex optimization to estimate conditional distributions.
problem Estimating uncertainty in predictions and posterior conditional distributions.
method Convex optimization of a posterior defined via non-linear transformations on Gaussians.
result CNR can fit arbitrary conditional distributions, including multimodal and non-symmetric ones.
Study shows pretraining and finetuning can effectively tackle covariate shift in linear regression.
problem Linear regression under covariate shift where source and target distributions differ but conditional distribution remains similar.
method Pretraining on source data and finetuning on target data using online SGD.
result Transfer learning with O ( N 2 ) O(N^2) O ( N 2 ) source data is as effective as supervised learning with N N N target data. Paper introduces data-dependent SSP for private linear and logistic regression.
problem Private linear and logistic regression with better performance.
method Data-dependent sufficient statistic perturbation (SSP) for linear and logistic regression.
result Data-dependent SSP outperforms state-of-the-art methods for linear and logistic regression.
We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We t…
Adversarial Regression is a proposition to perform high dimensional non-linear regression with uncertainty estimation. We used Conditional Generative Adversarial Network to obtain an estimate of the full predictive distribution for a new observation. Generative Adversarial Networks (GAN) are implicit generative models …
This paper extends transfer learning for linear regression to uncertain domain information.
problem Transfer learning for linear regression with uncertain domain information.
method A Dirichlet process is used to infer latent domain information from regression coefficients. A novel framework considers the joint distribution of variables.
result The proposed method controls bias better than previous pseudo-labelling approaches.
Study minimax linear regression under quantile risk, improving existing bounds and providing new results.
problem Designing minimax procedures in linear regression under quantile risk.
method Analyzes realizable setting with Gaussian noise, extends to all p-th power error functions, develops new lower and upper bounds.
result Proves minimaxity of a variant of the min-max regression procedure for all p-th power error functions.