Adversarial Contamination Meets Hard Thresholding: An Iterative Algorithm with Signal Adaptivity and Minimax Optimality

• URL: http://arxiv.org/abs/2606.27685v1
• Date: Fri, 26 Jun 2026 03:30:25 GMT
• Title: Adversarial Contamination Meets Hard Thresholding: An Iterative Algorithm with Signal Adaptivity and Minimax Optimality
• Abstract summary: Data contamination stemming from measurement errors, outliers, or corruption has motivated the development of robust statistical methods.<n>We propose a two-stage Ad-versa-resistant Iterative Harding (ACIHT) algorithm for logarithmic regression.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods. In this context, we propose a two-stage Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm for high-dimensional regression with contamination. Our nonconvex algorithm achieves minimax near-optimal (up to logarithmic terms) estimation by iteratively updating the coefficient vector and the contamination vector with different thresholding scales. We further demonstrate that our AC-IHT estimator is signal-adaptive: under proper signal conditions, it adaptively attains a sharper estimation rate and more accurate support recovery. Moreover, it enjoys the strong oracle property, laying a theoretical foundation for asymptotic inference. Numerical experiments confirm its superior finite-sample performance. Finally, we discuss theoretical extensions of the proposed procedure to generalized linear models and to heavy-tailed noise settings.

Related papers

• A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding [1.9336815376402718]
  This study proposes a novel low-rank approximation method that eliminates both prior rank specification and iterative optimization.<n>The method applies statistical singular value hard thresholding to each mode-wise unfolded matrix to automatically extract statistically significant components.<n> Simulation experiments demonstrate that the proposed method outperforms conventional approaches.
  arXiv  Detail & Related papers  (2025-05-09T17:30:16Z)
• Gradient Normalization Provably Benefits Nonconvex SGD under Heavy-Tailed Noise [60.92029979853314]
  We investigate the roles of gradient normalization and clipping in ensuring the convergence of Gradient Descent (SGD) under heavy-tailed noise. Our work provides the first theoretical evidence demonstrating the benefits of gradient normalization in SGD under heavy-tailed noise. We introduce an accelerated SGD variant incorporating gradient normalization and clipping, further enhancing convergence rates under heavy-tailed noise.
  arXiv  Detail & Related papers  (2024-10-21T22:40:42Z)
• Robust Stochastic Optimization via Gradient Quantile Clipping [6.2844649973308835]
  We introduce a quant clipping strategy for Gradient Descent (SGD) We use gradient new outliers as norm clipping chains. We propose an implementation of the algorithm using Huberiles.
  arXiv  Detail & Related papers  (2023-09-29T15:24:48Z)
• Conditional Denoising Diffusion for Sequential Recommendation [62.127862728308045]
  Two prominent generative models, Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs) GANs suffer from unstable optimization, while VAEs are prone to posterior collapse and over-smoothed generations. We present a conditional denoising diffusion model, which includes a sequence encoder, a cross-attentive denoising decoder, and a step-wise diffuser.
  arXiv  Detail & Related papers  (2023-04-22T15:32:59Z)
• Optimal Algorithms for the Inhomogeneous Spiked Wigner Model [89.1371983413931]
  We derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem. We identify in particular the existence of a statistical-to-computational gap where known algorithms require a signal-to-noise ratio bigger than the information-theoretic threshold to perform better than random.
  arXiv  Detail & Related papers  (2023-02-13T19:57:17Z)
• Tractable and Near-Optimal Adversarial Algorithms for Robust Estimation in Contaminated Gaussian Models [1.609950046042424]
  Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial method with a nonparametric discriminator. We develop tractable adversarial algorithms with simple spline discriminators, which can be implemented via nested optimization. The proposed methods are shown to achieve minimax optimal rates or near-optimal rates depending on the $f$-divergence and the penalty used.
  arXiv  Detail & Related papers  (2021-12-24T02:46:51Z)
• Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies [1.6457778420360534]
  A framework of outlier-resistant estimation is introduced to robustify arbitrarily loss function. A new technique is proposed to alleviate the requirement on starting point such that on regular datasets the number of data reestimations can be substantially reduced. The obtained estimators, though not necessarily globally or even globally, enjoymax optimality in both low dimensions.
  arXiv  Detail & Related papers  (2021-12-15T20:35:21Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• Adaptive filters for the moving target indicator system [10.152838128195468]
  Two approaches to improve the convergence of adaptive algorithms are presented. The proposed approach is based on an empirical signal to interference plus noise ratio (SINR) Its effectiveness is demonstrated using simulated data.
  arXiv  Detail & Related papers  (2020-12-31T04:22:55Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.