Related papers: Distributed randomized Kaczmarz for the adversaria…

Due to the ever growing amounts of data leveraged for machine learning and scientific computing, it is increasingly important to develop algorithms that sample only a small portion of the data at a time. In the case of linear least-squares,…

Deep neural networks have been shown to be vulnerable to adversarial examples---maliciously crafted examples that can trigger the target model to misbehave by adding imperceptible perturbations. Existing attack methods for k-nearest…

The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz (SSRK) is an variant of RK…

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential…

The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…

Distributed algorithms provide flexibility over centralized algorithms for resource allocation problems, e.g., cyber-physical systems. However, the distributed nature of these algorithms often makes the systems susceptible to…

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…

Machine learning algorithms are effective in several applications, but they are not as much successful when applied to intrusion detection in cyber security. Due to the high sensitivity to their training data, cyber detectors based on…

In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…

Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples,…

Randomization is a powerful tool that endows algorithms with remarkable properties. For instance, randomized algorithms excel in adversarial settings, often surpassing the worst-case performance of deterministic algorithms with large…

In this paper we address the computational feasibility of the class of decision theoretic models referred to as adversarial risk analyses (ARA). These are models where a decision must be made with consideration for how an intelligent…

Distributed diffusion is a powerful algorithm for multi-task state estimation which enables networked agents to interact with neighbors to process input data and diffuse information across the network. Compared to a centralized approach,…

In [Steinerberger, Q. Appl. Math., 79:3, 419-429, 2021] and [Shao, SIAM J. Matrix Anal. Appl. 44(1), 212-239, 2023], two new types of Kaczmarz algorithms, which share some similarities, for consistent linear systems were proposed. These two…

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…

This paper studies the problem of detecting adversarial perturbations in a sequence of observations. Given a data sample $X_1, \ldots, X_n$ drawn from a standard normal distribution, an adversary, after observing the sample, can perturb…

Adversarial Training is proved to be an efficient method to defend against adversarial examples, being one of the few defenses that withstand strong attacks. However, traditional defense mechanisms assume a uniform attack over the examples…