NTK neural networks are robust to adversarial attacks in nonparametric regression.
problem Adversarial robustness of neural networks in nonparametric regression.
method Gradient flow with early stopping for NTK neural networks, proving robustness in Sobolev spaces.
result NTK neural networks achieve optimal adversarial robustness rates in Sobolev spaces.
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.
Adversarial training improves linear regression solutions, revealing sparsity and abrupt interpolation.
problem Adversarial attacks on linear regression models.
method Formulated as a convex problem, adversarial training is used to find robust solutions that are sparse and interpolate data.
result Adversarial training with small disturbances gives the solution with the minimum-norm that interpolates the training data, revealing abrupt transition into interpolation.
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.
Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspe…
Adversarial training makes logistic regression weight loss landscapes sharper.
problem Understanding why adversarial training sharpens the weight loss landscape in logistic regression.
method Theoretical analysis of linear logistic regression model with L2 norm constraints, and experiments on ResNet18.
result Adversarial training sharpens the weight loss landscape in linear logistic regression models.
Study on robustness in linear regression models, focusing on adversarial perturbations.
problem Understanding and improving robustness in linear regression models to adversarial perturbations.
method Developed a two-stage adversarial learning framework that incorporates model structure information.
result Proved the consistency and developed the Bahadur representation of the adversarially robust estimator.
Paper develops robust Bayesian models for linear regression under adversarial perturbations.
problem Ensuring reliable machine learning models under data perturbations.
method Formulates adversarial Bregman divergence loss, computes adversarial perturbation, introduces adversarially robust posteriors, derives generalization certificates.
result Derives first rigorous generalization certificates for adversarially robust Bayesian linear regression.
Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we investigate the robustness of sparse regression models with strongly correlated co…
The paper analyzes how adversarial attacks affect sparse regression models.
problem Effects of adversarial attacks on sparse regression models.
method Primal-dual witness paradigm to analyze support of estimated regression parameter vector.
result Adversaries can influence sample complexity by corrupting irrelevant features.
Adversarial training improves linear regression solutions, offering robustness against small perturbations.
problem Vulnerability of linear models to adversarial perturbations.
method Formulated as a min-max problem, adversarial training minimizes the best solution under worst-case attacks.
result Adversarial training yields the minimum-norm interpolating solution in overparameterized models, equivalent to parameter shrinking methods in underparameterized models.
New method tackles adversarial sign-corrupted isotonic regression, estimating monotonic signals under heavy dependence.
problem Estimating monotonic signals when responses are sign-corrupted and adversarially designed to violate monotonicity.
method Developed ASCIFIT, a three-step estimation procedure using PAVA with pre- and post-processing corrections.
result Theoretical guarantees of sharp high probability upper bounds and minimax lower bounds for ASCIFIT.
Study on linear regression robustness to adversarial attacks.
problem Adversarial attacks on linear regression models.
method Analysis of prediction error bounds, asymptotic results, convex optimization.
result Adversarial error can grow to infinity with more features, while test error goes to zero.
New trade-off found between accuracy and adversarial robustness in regression.
problem Finding a balance between accuracy and robustness in regression models.
method Deriving a fundamental trade-off between standard and adversarial risk in regression with polynomial ridge functions.
result A necessary condition for achieving adversarial robustness without significant accuracy loss.
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.
DL models for MTS regression are vulnerable to adversarial attacks, posing risks in safety-critical applications.
problem Vulnerability of DL models to adversarial examples in MTS regression.
method Adversarial attack generation techniques from image classification were adapted for MTS.
result All state-of-the-art DL regression models (CNN, LSTM, GRU) are vulnerable to adversarial attacks.
Unified framework SVAM learns GLMs robustly to adversarial label corruption.
problem Learning GLMs under adversarial label corruption.
method SVAM framework based on variance reduction technique.
result Provable model recovery guarantees superior to state-of-the-art.
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
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.
New algorithms for regression with adversarial responses on various metric spaces.
problem Regression with adversarial responses under non-i.i.d. sequences.
method Proves universal consistency for a wide range of non-stationary processes.
result Achieves universal consistency for a broader class of sequences than stationary processes.
The paper detects adversarial examples in LECs for regression in CPS using variational autoencoder.
problem Detecting adversarial examples in learning-enabled cyber-physical systems (CPS).
method Inductive conformal prediction using a variational autoencoder regression model.
result The method effectively detects adversarial examples with a short delay in an emergency braking system simulation.
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
Efficient algorithms speed up adversarial training for linear models.
problem Adversarial training for linear models is computationally expensive.
method Tailored optimization algorithms for regression and classification.
result Significantly faster convergence rates for large-scale problems.
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.
Study improves H-consistency bounds for regression analysis.
problem Improving H-consistency bounds for regression analysis. method Generalized theorems and novel H-consistency bounds for various surrogate loss functions. result Derives principled surrogate losses for adversarial regression.
Adversarial weighting improves regression task adaptation.
problem Improving regression performance across domains with covariate shift.
method Adversarial network algorithm for instance weighting and task learning.
result The method enhances regression accuracy on target domains.
We propose two nonlinear regression methods, named Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for the general case of structural equation models. Both methods try to make the residual of regression independent from regressors while put…
Despite the considerable success enjoyed by machine learning techniques in practice, numerous studies demonstrated that many approaches are vulnerable to attacks. An important class of such attacks involves adversaries changing features at test time to cause incorrect predictions. Previous investigations of this proble…
The paper explores robustness in linear regression models under adversarial attacks.
problem The impact of test-time adversarial attacks on linear regression models.
method Quantitative estimates and phase transitions analysis.
result Precise characterization of tradeoffs between adversarial robustness and accuracy.
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.
Generative Adversarial Regression (GAR) learns risk scenarios robustly across policies.
problem Learning risk scenarios for conditional risk objectives.
method Generative adversarial framework for risk matching.
result GAR produces more stable and risk-preserving scenarios than baselines.
Interpolating estimators in nonparametric regression become suboptimal under adversarial attacks.
problem Adversarial robustness of interpolating estimators in nonparametric regression.
method Investigation of adversarial robustness of interpolating estimators in a nonparametric regression framework.
result Interpolating estimators must be suboptimal even under a subtle future X-attack. Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
The paper studies adversarial training for linear regression models.
problem Understanding the tradeoffs between robust and standard accuracy in adversarial training.
method Characterizes the fundamental tradeoff and specific adversarial training approach for linear regression with Gaussian features.
result Precise characterization of the standard and robust accuracy tradeoff in high-dimensional settings.
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.
Proposes a new method to improve regression models with reweighted samples.
problem Improves regression models' performance under low sample sizes and covariate perturbations.
method Reparametrizes sample weights using a doubly non-negative matrix and solves the reweighted estimate efficiently.
result Adversarial reweighting strategy delivers promising results on various datasets.
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.
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 …
Improved robust regression for heavy-tailed and contaminated data.
problem Linear regression with heavy-tailed and adversarially contaminated covariates and responses.
method Applying a filtering algorithm to covariates and then using Huber regression, least trimmed squares, or least absolute deviation estimators on the remaining data.
result Near-optimal error rates achieved for the Huber regression estimator.
The paper debiases machine learning predictions to correct bias in regression coefficients.
problem Bias in regression coefficients from machine learning predictions.
method Proposes an adversarial machine learning algorithm to de-bias predictions.
result Adversarial predictions recover true coefficients, while naive predictions are biased.
This paper examines how adversarial perturbations affect model performance and equilibrium learning.
problem Adversarial perturbations and covariate shifts impact model performance and equilibrium learning.
method Characterizes the extrapolation region in regression and classification, analyzes dynamics of adversarial learning games.
result Establishes two directional convergence results: a blessing in regression and a curse in classification.
Despite the tremendous success of deep neural networks in various learning problems, it has been observed that adding an intentionally designed adversarial perturbation to inputs of these architectures leads to erroneous classification with high confidence in the prediction. In this work, we propose a general framework…
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.
Study on online nonparametric regression using Sobolev kernel methods.
problem Adversarial nonparametric regression in high dimensions.
method Online kernelized ridge regression with Sobolev kernel analysis.
result Upper bounds on regret for Sobolev space classes, revealing optimality in certain cases.
Improved linear regression with privacy and robustness guarantees.
problem Private and robust linear regression with adversarial corruption.
method Differentially private stochastic gradient descent with full-batch gradient descent and adaptive clipping.
result Near optimal sample complexity for both private and robust linear regression.
Study robust regression learning under adversarial attacks.
problem Understanding which function classes are learnable in the presence of adversarial attacks.
method Introduced a novel agnostic sample compression scheme and used fat-shattering dimension to construct adversarially robust sample compression schemes.
result Finite fat-shattering dimension classes are learnable in both realizable and agnostic settings.
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.
We consider the non-parametric regression problem under Huber's ε-contamination model, in which an ε fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…