New framework for network regression models accounting for community structure.
problem Inaccurate modeling of residual dependencies in network regression models.
method Modeling errors as community-based and exploiting exchangeability properties.
result Parsimonious standard errors for regression parameters.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
Method detects errors in numerical data using regression models.
problem Noise and errors in numerical datasets.
method Introduced veracity scores and a filtering procedure for error detection.
result Method outperforms other approaches in identifying incorrect values.
Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the…
The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.
problem Improving loss function for deep neural network based vector-to-vector regression.
method Presenting performance bounds and new properties of MAE, deriving generalized upper bounds, and interpreting MAE as a Laplacian distribution.
result MAE is a more suitable loss function than MSE for DNN based vector-to-vector regression, especially when errors follow a Laplacian distribution.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under…
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
problem Regression with noisy and limited covariate data.
method Combines global Fréchet regression and principal component regression for low-rank structure.
result Improved efficiency and accuracy in high-dimensional and noisy data settings.
New ensemble SVM model reduces prediction error without choosing best kernel.
problem Reducing prediction error in regression problems.
method Bagged-weighted support vector regression model with random machines.
result Regression Random Machines achieve lower generalization error.
New GLS estimator handles high-dimensional data with autocorrelated errors.
problem High-dimensional regressions with autocorrelated errors.
method LASSO regression, autoregressive model fitting, and whitening.
result The method outperforms unadjusted LASSO in estimating errors driven by autoregressive processes.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We show that universal consistency of Empirical Risk Minimiza…
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation. The paper provides explicit formulas for those err…
Bayesian framework improves robustness in nonlinear regression models.
problem Measurement error, model misspecification, and distributional misspecification in regression analyses.
method Joint Dirichlet process prior on latent covariate-response distribution, updating with posterior pseudo-samples.
result Improved stability and consistency in estimators under increasing measurement error.
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 $Θ( rac{dM}{n})$.
Prevalidated ridge regression simplifies logistic regression for high-dimensional data.
problem Efficient probabilistic classification in high-dimensional data with logistic regression.
method Developed a prevalidated ridge regression model that matches logistic regression's performance but is more computationally efficient.
result Prevalidated ridge regression achieves similar classification error and log-loss to logistic regression for high-dimensional data.
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from the data. For N data points the computational demand is N2. Comparing the predic…
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 ℓ1-penalized Huber regression method. result Error bound identical to Gaussian case for L-subexponential covariates. This work precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.
problem Tradeoff between robustness and accuracy in adversarial training.
method Characterizes the effect of augmentation on standard error in linear regression; proves RST improves robust error without sacrificing standard error.
result RST improves both standard and robust error for neural networks under various perturbations.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
The paper examines prediction and estimation risks of ridgeless least squares under general error assumptions.
problem Prediction and estimation risks of ridgeless least squares under realistic error structures.
method Analysis of prediction and estimation risks under general regression error assumptions, including clustered or serial dependence.
result The benefits of overparameterization extend to time series, panel, and grouped data.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
Optimal machine learning requires interpolating training data in high-dimensional linear regression.
problem Achieving optimal predictive risk in overparameterized linear regression models.
method Analyzing proportional asymptotics of random design and label noise variance.
result Optimal performance in linear regression requires fitting training data to higher accuracy than inherent noise.
Bias correction needed after deep learning regression training.
problem Systematic error accumulation in deep learning regression models.
method Adjust bias of the machine learning model post-training.
result Bias correction efficiently solves error accumulation.
Study linear regression with missing or corrupted data, showing error bounds.
problem Linear regression under missing or corrupted data.
method Information-theoretic lower bounds and efficient algorithms.
result Error bounds match in missing and corruption settings.
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.
Study high-dimensional logistic regression with missing data, providing exact error characterizations.
problem High-dimensional logistic regression with missing or corrupted covariates.
method Exact characterizations of prediction and estimation errors under independence and moment conditions.
result Characterizations are universal and hold for various imputation strategies.
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…
CRUDE calibrates regression uncertainty without assuming specific error distributions.
problem Uncalibrated uncertainty estimates in regression models, especially for modern predictive tasks.
method CRUDE assumes error distributions have a constant shape, shifted and scaled by predicted mean and standard deviation.
result CRUDE produces sharper, better calibrated, and more accurate uncertainty estimates than existing methods.
The paper analyzes how data augmentation affects the test error in regression models.
problem Understanding the impact of data augmentation on the test error in regression models.
method Characterizes the test error in terms of population quantities and augmentation statistics.
result Provides a tight characterization of the test error in mean squared error.
Short proof shows how ridge regression works with random data.
problem Understanding prediction error in ridge regression with random design.
method Combination of exchangeability arguments, matrix perturbation, and operator convexity.
result Elementary proof of prediction error without complex inequalities.
A new error bound improves safety in Bayesian optimization.
problem Ensuring safety in Bayesian optimization with probabilistic models.
method Introducing a novel error bound using Wiener kernel regression for Gaussian processes and noise.
result The new error bound provides larger safety regions than previous methods.
This paper improves active learning for Gaussian process regression to handle distributional uncertainty.
problem Active learning for Gaussian process regression does not guarantee accurate predictions for target distributions.
method Proposes two methods to reduce worst-case expected error for Gaussian process regression.
result Shows an upper bound of the worst-case expected squared error, suggesting finite data labels can achieve arbitrarily small error.
Neural networks improve nonparametric regression with measurement errors.
problem Nonparametric regression with measurement errors.
method Proposes a neural network design using FNN, normalizing flow, and inference network.
result Neural network approach is more flexible and superior or comparable to classical methods.
Bayesian deep learning accounts for input uncertainty using Errors-in-Variables models.
problem Uncertainty in deep regression models, especially from input data.
method Bayesian treatment with Errors-in-Variables model to decompose predictive uncertainty.
result The approach yields more complete and consistent uncertainty estimates.
New weighted Lasso estimates improve logistic regression performance with measurement error.
problem Improper Lasso estimates in sparse logistic regression with equal penalties.
method Proposed weighted Lasso estimates using McDiarmid inequality for non-asymptotic oracle inequalities.
result Finite sample behavior illustrated by non-asymptotic oracle inequalities for estimation and prediction errors.
A visualization aids in comparing regression models by highlighting errors and correlations.
problem Comparing regression models is difficult due to varying hyper-parameters and metrics.
method Introduces a novel visualization approach using 2D residual space, Mahalanobis distance, and colormaps.
result Enhanced understanding of regression model performance differences and error distributions.
Develops a method for kernel ridge regression under covariate shift using pseudo-labels.
problem Learning a regression function with small mean squared error over a target distribution with labeled data from a different feature distribution.
method Split labeled data into two subsets, conduct kernel ridge regression on each, use imputation model to fill missing labels, and select the best candidate model.
result Non-asymptotic excess risk bounds demonstrate effective adaptation to target distribution and covariate shift.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
Scaling laws in linear regression explain model performance improvements with size and data.
problem Disagreement between empirical neural scaling laws and conventional wisdom on variance error.
method Infinite dimensional linear regression setup, one-pass SGD, Gaussian prior, power-law spectrum.
result Variance error is dominated by other errors, disappearing from the bound due to SGD's implicit regularization.
This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via …
The study examines Kernel Ridge Regression error rates across noiseless and noisy conditions.
problem Characterizing Kernel Ridge Regression error rates in different noise levels.
method Unified analysis of Kernel Ridge Regression under various noise and regularization conditions.
result A crossover from noiseless to noisy error rates is observed as sample complexity increases.
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
Novel bounds for logistic regression coreset construction and feature selection.
problem Efficiently summarize and reduce logistic regression inputs.
method Feature space sketching for logistic regression.
result Tight bounds for coreset construction and feature selection.
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data t…
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.
Gaussian process regression helps approximate Bayesian inverse problems efficiently.
problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2-norm error between true and approximate likelihood.