Unified framework for sparse logistic regression with nonconvex regularization.
problem Sparse logistic regression with nonconvex regularization.
method Unified framework, line search criteria for nonconvex terms.
result Effective classification and feature selection at lower computational cost.
We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.
problem Analyzing coresets for regularized regression problems.
method Examined coresets for ridge regression and proposed a modified lasso problem.
result No coreset for regularized regression can be smaller than the unregularized version when reqs. Investigates methods to regularize quantile regression for accurate predictions.
problem Improving accuracy and fairness in quantile regression predictions.
method Various regularization techniques including expected pinball loss, monotonicity constraints, and rate constraints.
result Deep lattice networks can maintain non-crossing quantiles and improve calibration and fairness.
Paper explores how DPP sampling can implicitly regularize kernel regression.
problem Improving kernel regression by reducing redundancy in data.
method Using Determinantal Point Processes (DPPs) to sample subsets implicitly regularizes ridgeless Kernel Regression.
result Ensemble of ridgeless regressors can be effective for datasets with redundant information.
Efficiently performs robust and sparse kernel regression.
problem Robust and sparse kernel regression.
method Sign gradient descent and early stopping.
result Sign gradient descent achieves robust and sparse kernel regression efficiently.
Safe screening rules reduce computation time in logistic regression with ℓ0−ℓ2 regularization.
problem Efficiently solving logistic regression with many features and regularization.
method Screening rules based on Fenchel dual lower bounds of strong conic relaxations.
result A high percentage of features can be safely removed before solving, leading to substantial speed-up.
In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the process finds quantifications for the categories that are optimal for the regres…
Study introduces a new method for multiple parameter regularization in polynomial functional regression.
problem Handling varying regularization parameters in polynomial functional regression.
method Developed a theoretically grounded algorithm for multiple parameter regularization and model aggregation.
result Promising results from evaluations on synthetic and real-world data.
Regularized linear regression improves binary classification performance, especially with ridge and ℓ1 regularization.
problem Improving binary classification accuracy with noisy labels.
method Systematic study of regularization strengths on linear classifiers trained on noisy binary classification data.
result Ridge regression consistently improves classification error, while ℓ1 regularization can induce sparsity and ℓ∞ regularization can concentrate weights to two values. Paper develops a new method for distribution regression with indefinite kernels.
problem Distribution regression with indefinite kernels.
method Coefficient-based regularized distribution regression with two-stage sampling.
result Optimal learning rates derived for the algorithm under mild conditions.
Adaptive sparseness enhances robust regression using MCC and ARD.
problem Developing a robust regression method with adaptive sparseness.
method Integrating MCC with ARD in a Bayesian framework using variational Bayesian inference.
result MCC-ARD regression outperforms existing methods in prediction and feature selection.
A neural network solves logistic regression with ℓ1 regularization efficiently.
problem Efficiently solving logistic regression with ℓ1 regularization due to non-differentiability of ℓ1 norm. method A simple projection neural network that avoids auxiliary variables and smooth approximations.
result The neural network converges to a solution of the problem with any initial value and outperforms existing methods.
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, and high-dimensional analysis. We propose a broad framework…
Unified framework for accurate coresets in latent variable models and regularized regression.
problem Efficiently training models on large datasets.
method Unified framework for constructing accurate coresets for latent variable models and ℓp-regularized regression. result Unified framework reduces coreset size for latent variable models and ℓp-regularized regression. Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected beha…
Solving logistic regression with L1-regularization in distributed settings is an important problem. This problem arises when training dataset is very large and cannot fit the memory of a single machine. We present d-GLMNET, a new algorithm solving logistic regression with L1-regularization in the distributed settings. …
NA0CT2 improves tensor regression predictions with ℓ0 regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented ℓ0 regularization on Tucker decomposition. result Achieves exact ℓ0 regularization on core tensor in linear and generalized linear tensor regression. SGD implicitly regularizes linear regression problems better than ridge regression for many cases.
problem Understanding implicit regularization in linear regression problems.
method Comparing SGD and ridge regression on a broad class of least squares problems.
result SGD generalizes no worse than ridge regression for many problem instances, sometimes better.
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.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
A new method for linear regression using feature graphs and hierarchical shrinkage.
problem Estimating robust parameters for linear regression models.
method Hierarchical Feature Regression (HFR) estimator that constructs a supervised feature graph to shrink parameters towards group targets.
result Demonstrates good predictive accuracy and versatility compared to other regularization techniques.
Improves calibration of regression models without requiring additional data.
problem Poor calibration of regression models leading to unreliable predictions.
method Quantile regularizer based on cumulative KL divergence.
result Significantly improves calibration for regression models trained with Dropout VI and Deep Ensembles.
The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years. A common feature of this work is that the adversarial robustification often corresponds exactly to regularization methods whi…
Enhances tensor regression for interpretability and performance.
problem Interpreting and modeling multidimensional tensor data with structural heterogeneity.
method Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR) with hybrid regularization and nonnegativity constraints.
result NS-KTR outperforms conventional methods in synthetic and real hyperspectral datasets.
Improved regression analysis using Padé approximants with new residuals and regularization.
problem Improving regression analysis with Padé approximants for accuracy and avoiding overfitting.
method New residuals in least squares method, system of linear equations for rational functions, Tikhonov regularization.
result Demonstrated efficiency in practical cases from physics and reliability theory.
Enhances KLR for indefinite kernels with L1-norm regularization.
problem Classifying with indefinite kernels captures more domain-specific information.
method Introduces L1-norm regularization to induce sparsity and a proximal linearized algorithm. result Superior performance in accuracy and sparsity on multiple datasets.
Improved robustness in multivariate regression and classification with DRO under Wasserstein metric.
problem Outliers in covariates and responses.
method Distributionally Robust Optimization (DRO) with Wasserstein metric ambiguity set and regularization.
result Significant improvement in predictive error and robustness.
This paper proposes robust matrix variate regression models with rank constraints and vector regularization.
problem High dimensional and noisy matrix-valued predictors in regression models.
method Rank constraint, vector regularization, alternating projected gradient descent algorithm.
result The proposed method achieves the minimax rate of estimation errors.
The paper proposes a gradient-based method for multi-penalty Ridge regression.
problem Optimizing multiple regularization hyperparameters for linear regression.
method Gradient-based optimization through matrix differential calculus.
result The method outperforms traditional regularization techniques like LASSO and Ridge.
The paper identifies conditions for trend reversal in classification tasks.
problem Trend reversal in classification scores and dataset values.
method Algebraic conditions and numerical results for ridge regression.
result Existence of pathological regularization regimes for certain dataset conditions.
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a …
In this paper, we investigate a multivariate multi-response (MVMR) linear regression problem, which contains multiple linear regression models with differently distributed design matrices, and different regression and output vectors. The goal is to recover the support union of all regression vectors using l1/l2-reg…
MGD with early stopping tends to ridge regularization in least squares regression.
problem Characterizing the implicit regularization of MGD with early stopping.
method Continuous-time view of MGD (momentum gradient flow) and comparison with explicit ridge regularization.
result Under optimal tuning, the risk of MGF is no more than 1.54 times that of ridge.
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistica…
The paper examines how adversarial training and noise affect neural network performance.
problem Overfitting in adversarial training and data augmentation.
method Adversarial training and data augmentation with noise in the context of regularized regression in RKHS.
result Appropriate regularization can prevent overfitting and improve performance.
Unified approach to linear regression using covariance fitting for optimal weights.
problem Finding optimal weights for linear regression models when weights are unknown.
method Covariance fitting SPICE-methodology to obtain data-adaptive weights.
result Tuned versions of known regularized estimators are unified under a common approach.
Improves robustness of high-dimensional regression with rank objective and group lasso regularization.
problem Heavy-tailed noise and outliers in high-dimensional regression.
method Non-smooth Wilcoxon score based rank objective, group lasso regularization, data-driven tuning rule, proximal augmented Lagrangian method.
result Robust estimator with finite-sample error bound and efficient computational method.
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the output functions learnt from these blocks. Since the average process will decrease th…
Critic-regularized regression improves offline RL performance.
problem Poor performance of off-policy algorithms in offline RL.
method Critic-regularized regression (CRR) for policy learning from fixed datasets.
result CRR outperforms state-of-the-art offline RL algorithms significantly.
The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.
problem Characterizing generalization properties of high-dimensional kernel ridge regression.
method Bias-variance decomposition of the expected excess risk, considering different regularization schemes and data eigen-profiles.
result The risk curve of kernel regression can be double-descent-like, bell-shaped, or monotonic, depending on n, d, and regularization level.
Optimal ridge regularization computed iteratively from generative parameters.
problem Finding the optimal ridge regularization strength for linear regression.
method Iterative procedure to compute optimal regularization strength numerically.
result The proposed procedure attains near-optimal generalization across various conditions.
Unified theory for kernel regression generalizes well under realistic assumptions.
problem Analyzing kernel regression under realistic conditions.
method Unified theory providing rigorous bounds for various settings.
result Self-regularization phenomenon in kernel matrices enables good generalization.
Optimizes hyperparameter tuning for models using approximate leave-one-out cross-validation.
problem Finding optimal hyperparameters for regularized models using approximate leave-one-out cross-validation.
method Derive efficient formulas for gradient and hessian of approximate leave-one-out cross-validation, apply second-order optimization.
result Demonstrates the effectiveness of the approach on real-world data sets.
The paper improves confidence ellipsoids for ridge regression with PAC bounds.
problem Uncertainty quantification in ridge regression for insufficiently exciting inputs.
method Extension of SPS EOA algorithm to ridge regression with PAC bounds.
result Explicitly shows how regularization parameter affects region sizes and provides tighter bounds.
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…
New algorithms solve large-scale convex regression problems.
problem Large-scale convex regression with subgradient regularization.
method Active set type algorithm on dual QP, approximate optimization, randomized augmentation.
result Solves problems with n=10^5 and d=10 in minutes.
FALL improves local model training with anchor regularization.
problem Efficient local model training in regression tasks.
method Regularization with precomputed anchor models, closed-form solution.
result FALL outperforms network Lasso in accuracy with significantly less training time.
GD outperforms ridge regression and SGD in linear regression problems.
problem Comparing the risks of GD, ridge regression, and SGD in linear regression problems.
method Instance-wise finite-sample risk analysis of GD, ridge regression, and SGD.
result GD outperforms ridge regression and is incomparable with SGD in some cases.