Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
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.
Paper tackles robust matrix completion with heavy-tailed noise.
problem Estimating a low-rank matrix from noisy incomplete data.
method Adaptive Huber loss for robustness, nonconvex algorithm with spectral initialization.
result Achieves minimax-optimal statistical estimation error under bounded second moment condition.
New robust estimator improves variable selection and coefficient estimation in linear regression with heavy-tailed errors and outliers.
problem Heavy-tailed errors and anomalous predictors in high-dimensional regression.
method Adaptive PENSE estimator for robust variable selection and estimation.
result Adaptive PENSE estimator provides reliable results even under very heavy-tailed errors and aberrant predictors.
New bounds link SGD's generalization to heavy tails without topological assumptions.
problem Linking SGD's generalization error to heavy tails without additional assumptions.
method Developed Wasserstein stability bounds for heavy-tailed SDEs and their discretizations, converting to generalization bounds.
result Generalization bounds for a broader class of objective functions, including non-convex functions, without topological assumptions.
Study shows heavy-tailed distributions affect reliability of machine learning calibration statistics.
problem Reliability of calibration statistics for machine learning regression tasks is affected by heavy-tailed uncertainty and error distributions.
method Examined two calibration error estimation methods (CE and ZMS) and found ZMS to be less sensitive to heavy-tailed distributions.
result Heavy-tailed distributions make MSE and MV unreliable, but ZMS remains a reliable approach.
Work on SGDm under heavy-tailed noise, revealing its generalization properties.
problem Understanding generalization of SGDm under heavy-tailed noise.
method Analysis of continuous-time limit (SDE) and discrete-time SGDm, establishing generalization bounds.
result SGDm can have worse generalization in the presence of heavy-tailed noise for quadratic loss functions.
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.
Proposes a robust method for high-dimensional linear models.
problem Inference in high-dimensional settings with heavy-tailed errors and clustered data.
method Residual randomization procedure for Lasso-based inference.
result Outperforms state-of-the-art methods in challenging settings.
COS method convergence conditions expanded for heavy-tailed distributions.
problem Ensuring convergence of the COS method for various densities.
method Analyzing truncation error and providing conditions for convergence.
result Conditions for COS method convergence extended to include heavy-tailed distributions.
Study improves robust nonparametric regression in heavy-tailed noise.
problem Robust nonparametric regression with heavy-tailed noise and unbounded functions.
method Huber regression in reproducing kernel Hilbert spaces (RKHS), probabilistic effective hypothesis space, new comparison theorems.
result Explicit finite-sample error bounds and convergence rates for Huber regression in RKHS under heavy-tailed noise.
Markov chain decoders improve generative models' ability to produce heavy-tailed data.
problem Generative models struggle with heavy-tailed distributions.
method Replaced Gaussian decoder with Markov chain-based Phase-Type distributions.
result Significantly reduced tail Kolmogorov-Smirnov distance and extreme quantile error.
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.
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. Paper quantizes heavy-tailed data for near optimal estimation rates.
problem Estimating parameters from heavy-tailed data with quantization.
method Truncate and dither data, then uniformly quantize; achieves near minimax rates.
result Near optimal estimation rates achievable with quantized data.
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …
New study reveals how heavy-tailed SGD dynamics lead to compressible neural networks.
problem Understanding why large neural networks can be compressed effectively.
method Linking SGD dynamics to compressibility properties of neural networks.
result Large step-size/batch-size ratios and overparametrization lead to heavy-tailed SGD dynamics, making networks compressible.
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.
Study uses spectral risk for learning with heavy-tailed data.
problem Learning with heavy-tailed loss distributions.
method Spectral risk with Lipschitz-continuous density, derivative-free learning.
result Excess risk guarantees and improved performance over traditional methods.
The study analyzes how covariance estimation errors affect the global minimum-variance portfolio under heavy-tailed distributions.
problem The impact of covariance estimation errors on the global minimum-variance portfolio under heavy-tailed distributions.
method Characterization of covariance-estimation error's effect on GMVP suboptimality, derivation of regret identity and bound, application to heavy-tailed returns.
result The decision geometry of GMVP regret is invariant to a (p-1)-dimensional projection of the error matrix, with invariance to the covariance-scale direction as an exact special case.
Study on estimating rank-one tensors in noisy data with heavy tails.
problem Estimating rank-one spiked tensors in the presence of heavy tailed errors.
method Analysis of spectral norm of random tensors with iid entries.
result Signal strength requirements for optimal estimation are similar for heavy tailed and Gaussian noise, but vanish for noise with finite fourth moment.
Studied how heavy-tailed behavior affects SGD's generalization in quadratic optimization.
problem Link between heavy-tailed behavior and generalization in SGD.
method Used heavy-tailed stochastic differential equation and proved stability bounds.
result Stability of SGD depends on the loss function's tail behavior.
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
problem Sparse learning for high-dimensional heavy-tailed locally stationary time series.
method Additive modeling with kernel smoothing, sparsity-inducing penalized estimation.
result Prediction-error bounds and convergence rates for different sparsity structures.
Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.
problem Optimizing convex and Lipschitz functions with heavy-tailed noise.
method Develops tail bounds for optimization error of Stochastic Mirror Descent.
result Tail bounds extend to heavier-tailed noise regimes without diameter constraints.
The paper explores how benign overfitting occurs in heavy-tailed input distributions.
problem Understanding overfitting in heavy-tailed input distributions.
method Analysis of maximum margin classifiers on unregularized logistic loss with gradient descent.
result Linear classifiers trained under certain conditions can asymptotically achieve the noise level as misclassification error.
Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.
problem Challenges of classical Lasso in handling heavy-tailed noise and outliers.
method Data-augmented soft-thresholding with Student's t-distribution loss.
result Heavy Lasso achieves comparable rates to Huber loss under theoretical bounds.
Paper tackles DP-SCO with heavy-tailed data in high dimensions, improving error bounds.
problem Differentially private stochastic optimization with heavy-tailed data in high-dimensional spaces.
method Proposes methods for DP-SCO with polytope constraints and LASSO, analyzing sparsity constraints.
result Achieved near optimal error bounds for DP-SCO with heavy-tailed data.
Bayesian method selects important covariates in modal regression.
problem Bayesian modal regression with heavy-tailed responses.
method Expectation-maximization algorithm for parameter estimation; test statistic for variable selection.
result Efficacy of the proposed method in identifying important covariates.
Efficiently estimates sparse mean from heavy-tailed data.
problem Robustly estimating sparse mean from heavy-tailed distributions.
method Stability-based approach adapted for heavy-tailed data.
result Optimal sample complexity with logarithmic dependence on dimension.
New approach achieves optimal rates for differentially private stochastic convex optimization with heavy-tailed gradients.
problem Differentially private stochastic convex optimization with heavy-tailed gradients.
method Reduction-based approach to achieve optimal rates.
result Achieved optimal rates up to logarithmic factors, nearly matching a lower bound.
We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian inequalities in order to derive a robust risk estimator, which by design is easy to …
The paper investigates heavy-tailed behavior in offline SGD, showing it approximates power-law tails.
problem Understanding heavy-tailed behavior in offline (multi-pass) SGD with finite data.
method Proves nonasymptotic Wasserstein convergence bounds for offline SGD to online SGD.
result Offline SGD exhibits approximate power-law tails as the number of data points increases.
New algorithm guarantees performance on noisy data.
problem Learning with noisy data and heavy-tailed distributions.
method Anytime online-to-batch conversion for smooth objectives.
result Stochastic gradient-based algorithm with sub-Gaussian error bounds.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
AdapDISCOM tackles high-dimensional multimodal data with missingness and errors, improving prediction and biomarker selection.
problem High-dimensional multimodal data with block-wise missingness and measurement errors.
method AdapDISCOM introduces modality-specific weighting schemes to address heterogeneity and error magnitudes.
result AdapDISCOM consistently outperforms existing methods under heterogeneous contamination and heavy-tailed distributions.
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
New SGD variant makes neural networks compressible without assumptions.
problem Improving neural network compressibility without strong assumptions.
method Introducing heavy-tailed noise to SGD iterates.
result Compressible outputs with high probability for any compression rate.
This work analyzes CVaR under heavy-tailed data, providing generalization and robustness bounds.
problem Understanding CVaR's behavior under heavy-tailed data and rare high-impact losses.
method Learning-theoretic analysis of CVaR-based empirical risk minimization.
result Sharp, high-probability generalization and excess risk bounds under minimal moment assumptions.
Study learns linear system dynamics from noisy bilinear data.
problem Learning linear dynamics from bilinear observations with process and measurement noise.
method Regression with Kronecker product design, data-dependent and independent error bounds.
result Upper bounds on statistical error rates and sample complexity for learning dynamics matrices.
Improved Clipped-SGD achieves near-optimal heavy-tailed statistical estimation in streaming settings.
problem High-dimensional heavy-tailed statistical estimation in streaming with memory constraints.
method Stochastic convex optimization with Clipped-SGD, proving near-optimal sub-Gaussian statistical rates.
result Clipped-SGD achieves an error of T r ( Σ ) + T r ( Σ ) ∥ Σ ∥ 2 log ( log ( T ) δ ) T \sqrt{\frac{\mathsf{Tr}(Σ)+\sqrt{\mathsf{Tr}(Σ)\|Σ\|_2}\log(\frac{\log(T)}δ)}{T}} T Tr ( Σ ) + Tr ( Σ ) ∥Σ ∥ 2 l o g ( δ l o g ( T ) ) with probability 1 − δ 1-δ 1 − δ . Maximal concentration bounds for stochastic approximation with heavy-tailed noise.
problem Analyzing the convergence of stochastic approximation algorithms under heavy-tailed Markovian noise.
method Novel Lyapunov function and black-box truncation argument.
result Tail behavior of the error can be sub-Gaussian, sub-Weibull, or lighter than any Pareto but heavier than any Weibull.
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.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
This paper improves kernel quantile regression with random features for handling heavy-tailed noises.
problem Handling heavy-tailed noises in kernel quantile regression.
method Introduces a refined error decomposition and establishes a novel connection between KQR-RF and KRR-RF.
result Establishes capacity-dependent learning rates for KQR-RF under mild conditions on the number of random features, which are minimax optimal up to some logarithmic factors.
TSLiNGAM improves causal discovery in heavy-tailed data.
problem Identifying causal relationships in data with heavy tails.
method Combines DAGs with structural causal models, leveraging non-Gaussian noise.
result Significantly better performance on heavy-tailed and skewed data.
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.
problem Stochastic multi-armed bandits with heavy-tailed rewards.
method Proposes a novel robust estimator and perturbation-based exploration strategy.
result Develops upper and lower regret bounds for various perturbations.
Proposes a transfer learning method for high-dimensional quantile regression.
problem Inadequate handling of heterogeneity and heavy tails in transfer learning.
method High-dimensional quantile regression framework with double transfer learning estimator.
result Established error bounds and valid confidence intervals for high-dimensional quantile regression coefficients.