We find the optimal error for a constrained regression model under a linear model.
problem Minimizing error while adhering to demographic parity constraints.
method Proposed a minimax optimal error analysis for a demographic parity-constrained regression problem within a linear model.
result The minimax optimal error is characterized by $Θ( rac{dM}{n})$.
This paper analyzes how machine learning models resist adversarial attacks in nonparametric regression.
problem Adversarial attacks on machine learning models in nonparametric regression.
method Theoretical analysis of minimax rates of convergence under adversarial sup-norm.
result The minimax rate under adversarial attacks is the sum of two terms: standard rate and deviation of true function.
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.
New estimator achieves minimax optimal risk in transfer learning.
problem Nonparametric regression with transfer learning.
method Confidence thresholding estimator and data-driven adaptive algorithm.
result Adaptive algorithm achieves minimax risk up to a logarithmic factor.
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.
Paper finds a lower bound for estimating low-rank matrices in logistic regression.
problem Estimating low-rank coefficient matrices in logistic regression.
method Derives a minimax lower bound on the risk.
result The bound depends on matrix dimensions, rank, and sample size.
Meta-theorems validate fair regression algorithms under demographic parity constraints.
problem Regression under demographic parity constraints.
method Meta-theorems and post-processing methods.
result Fair minimax optimal regression can be achieved through post-processing.
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
Study on kernel regression risk in high dimensions using Pinsker bound.
problem Kernel regression risk in high-dimensional inner product spaces.
method Investigation of Pinsker bound for kernel regression on sphere Sd with sample size n=αdγ(1+od(1)). result Exact minimax risk and Pinsker constant identified for kernel regression.
Paper tackles adversarial attacks on nonparametric regression models.
problem Vulnerability of machine learning models to adversarial attacks in nonparametric regression.
method Establishes minimax rate and proposes adaptive estimators for robust nonparametric regression under adversarial Lq-risks. result Achieves minimax optimality and provides adaptive estimators for robust nonparametric regression.
Study improves distributional regression evaluation with CRPS, finding optimal rates of convergence.
problem Improving probabilistic forecasts in meteorology using distributional regression.
method Extends theoretical properties of CRPS evaluation to include covariates and finite sample sizes, analyzing convergence rates for different methods.
result Optimal minimax rate of convergence for distributional regression methods is achieved by k-nearest neighbor and kernel methods.
The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.
problem High-dimensional additive regression with heavy-tailed errors and transfer learning.
method Smooth backfitting estimator with local linear smoothing, followed by a two-stage estimation method.
result The method achieves the minimax optimal rate under certain conditions.
Transformers can efficiently approximate nonparametric regression with minimal parameters and sequences.
problem Efficiently approximating nonparametric regression functions with transformers.
method Kernel-weighted polynomial basis and gradient descent.
result Achieves minimax optimal rate of convergence with fewer parameters and sequences.
ConquerNet smooths quantile regression for deep learning with minimax guarantees.
problem Optimization challenges in quantile regression for deep models.
method ConquerNet uses convolution-smoothed quantile ReLU neural networks.
result ConquerNet provides minimax guarantees and outperforms standard quantile neural networks.
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.
Study shows rates for Laplacian-eigenmap methods in nonparametric regression.
problem Minimizing error in nonparametric regression using Laplacian-eigenmap.
method Adaptive and non-adaptive minimax rates using Sobolev space constraints.
result Extends minimax rates to various weighted Laplacian matrices.
Modified ReLU networks improve regression estimation rates.
problem Regression estimation with smooth functions.
method Using modified ReLU neural networks with specific weight modifications.
result Empirical risk minimizers achieve minimax rate of prediction.
Study on deep learning for speckle noise reduction in imaging modalities.
problem Multiplicative speckle noise challenges conventional deep learning methods for speckle denoising.
method Likelihood-based deep neural network (DNN) estimators for nonparametric regression under speckle noise.
result Established minimax rates for speckle denoising, matching those for additive Gaussian noise alone.
Quantile regression with ReLU networks achieves minimax rates for various function types.
problem Estimating quantiles from covariates with neural networks.
method Quantile regression with rectified linear unit (ReLU) neural networks.
result ReLU networks achieve minimax rates for broad collections of function types.
Paper studies minimax optimal regression using Laplacian smoothing over graphs.
problem Minimax optimal regression over Sobolev spaces.
method Laplacian smoothing on neighborhood graphs.
result Upper bounds match minimax optimal rates for first-order Sobolev class.
The paper optimizes k-NN for distributed learning with minimax optimal performance.
problem Minimizing error rates in classification, regression, and density estimation.
method Optimal aggregation of fixed-k nearest neighbors from multiple subsets of data.
result Achieves minimax optimal error rates up to a logarithmic factor.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has bounded support and the probability density function is bounded away from zero in i…
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L2-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Paper proposes a new method for regression using optimal transport cost optimization.
problem Regression problem, especially with complex noise forms.
method Directly optimizes the optimal transport cost between true and estimated distributions.
result Achieves state-of-the-art results on various datasets.
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of parameters are precisely non-zero. This excludes models where linear formulations…
Develops high-probability minimax quantile bounds for statistical problems.
problem Statistical procedures often lose information about tail behavior when reduced to expectations.
method Introduces minimax quantiles, develops high-probability variants of minimax methods, and converts risk lower bounds to quantile lower bounds.
result Obtains high-probability minimax quantile lower bounds for various statistical problems.
PCR-LE achieves optimal rates for nonparametric regression over Sobolev spaces.
problem Nonparametric regression over Sobolev spaces with random design.
method PCR-LE using Laplacian Eigenmaps on neighborhood graphs.
result PCR-LE achieves minimax rates of convergence for both estimation and goodness-of-fit testing.
GL-LowPopArt improves minimax-optimal estimation for trace regression.
problem Minimizing estimation error in generalized low-rank trace regression.
method Two-stage approach: nuclear norm regularization followed by matrix Catoni estimation.
result Achieves instance-wise optimal error bounds up to condition number.
Kernel method improves instrumental variable regression rates.
problem Nonparametric instrumental variable regression with weak instruments.
method Kernel-based two-stage least-squares method, strong L2 convergence analysis. result Minimax optimal rates for instrumental regression under standard assumptions.
The paper improves Gaussian process regression by optimizing hyperparameters.
problem Hyperparameter tuning for Gaussian process regression models.
method Adaptive sparse variational approximations using variational Bayes.
result Minimax optimal rates of convergence for variational posterior.
Study on regression with Markovian data, establishing limits and proposing an improved algorithm.
problem Least squares regression with dependent Markovian data.
method Sharp information theoretic lower bounds, analysis of SGD-DD and SGD, experience replay algorithm.
result Experience replay algorithm outperforms SGD-DD in Markovian data regression.
Deep neural networks can learn smooth functions without parameters.
problem Learning smooth functions from shallow ReLU neural networks.
method Using over-parameterized shallow ReLU neural networks with norm constraints.
result Least squares estimators based on shallow neural networks are minimax optimal.
Novel quasi-Bayesian method for IV regression using machine learning models.
problem Uncertainty quantification in IV regression with machine learning models.
method Quasi-Bayesian procedure based on kernelized IV models and dual formulation.
result Established minimax optimal contraction rates and scalable inference algorithm.
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.
Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.
problem Gaussian process regression struggles with compositional functions.
method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.
result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…
GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.
problem The suboptimality of GP-UCB under polynomial effective optimism.
method Analysis of effective optimism level and new regret lower bound.
result GP-UCB is not minimax optimal under polynomial growth of effective optimism.
Personalizes pre-trained models for nonparametric regression with limited data.
problem Improving data efficiency in nonparametric regression with few samples.
method Develops a theoretical framework and algorithms for few-shot personalization of black-box models.
result Achieves minimax optimal rate for personalization in nonparametric regression.
A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have…
Study on optimal rate of kernel regression for large-dimensional data.
problem Characterizing the upper and lower bounds of kernel regression for large-dimensional data.
method Using Mendelson complexity and metric entropy, the study characterizes the upper and lower bounds of kernel regression for large-dimensional data.
result The minimax rate of the excess risk of kernel regression is \( n^{-1/2} \) for \( n \asymp d^γ \) with \( γ=2, 4, 6, 8, \cdots \).
This paper studies robust regression in the settings of Huber's ε-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of ε-contamination models for various regression problems including nonpa…
The paper studies the benefits of curriculum learning in linear regression tasks.
problem Theoretical understanding of curriculum learning's benefits in machine learning.
method Theoretical analysis of curriculum learning in structured and unstructured multitask linear regression problems.
result Adaptive learning in the unstructured setting is fundamentally harder than oracle learning, but not in the structured setting.
Proposes online debiasing estimators for adaptive linear regression.
problem Adaptive data collection leads to non-normal asymptotic behavior in simple methods.
method Online debiasing estimators that correct distributional anomalies.
result Asymptotic normality and minimax lower bound for proposed estimators.
We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.
New method estimates minimizer and minimum value of a regression function.
problem Estimating minimizer and minimum value of a regression function from noisy data.
method Projected gradient descent with gradient estimated by regularized local polynomial algorithm, followed by a rate optimal nonparametric procedure.
result Achieves minimax optimal rates of convergence for smooth and strongly convex functions.
New algorithm resists contamination in high-dimensional regression with optimal performance.
problem Adversarial and measurement errors in high-dimensional data.
method Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm.
result Achieves minimax near-optimal estimation and signal-adaptive support recovery.