Related papers: Robust blind methods using $\ell_p$ quasi norms

Motivated by $\ell_p$-optimization arising from sparse optimization, high dimensional data analytics and statistics, this paper studies sparse properties of a wide range of $p$-norm based optimization problems with $p > 1$, including…

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…

While deep neural networks are sensitive to adversarial noise, sparse coding using the Basis Pursuit (BP) method is robust against such attacks, including its multi-layer extensions. We prove that the stability theorem of BP holds upon the…

The robust self-training (RST) framework has emerged as a prominent approach for semi-supervised adversarial training. To explore the possibility of tackling more complicated tasks with even lower labeling budgets, unlike prior approaches…

We consider the problem of determining the asymptotic order of the Gelfand numbers of mixed-(quasi-)norm embeddings $\ell^b_p(\ell^d_q) \hookrightarrow \ell^b_r(\ell^d_u)$ given that $p \leq r$ and $q \leq u$, with emphasis on cases with…

We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach-Mazur rotation…

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is…

In this study, we focus on computing the projection onto the $\ell_p$ quasi-norm ball, which is challenging due to the non-convex and non-Lipschitz nature inherent in the $\ell_p$ quasi-norm with $0<p<1$. We propose a novel localized…

In its vast majority entanglement verification is examined either in the complete characterized or totally device independent scenario. The assumptions imposed by these extreme cases are often either too weak or strong for real experiments.…

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the…

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that…

Robust learning from noisy demonstrations is a practical but highly challenging problem in imitation learning. In this paper, we first theoretically show that robust imitation learning can be achieved by optimizing a classification risk…

Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ $L_p$-norm ($0<p<1$) regularization to induce sparsity and…

Detecting anomalies in musculoskeletal radiographs is of paramount importance for large-scale screening in the radiology workflow. Supervised deep networks take for granted a large number of annotations by radiologists, which is often…

Deep neural networks perform well on real world data but are prone to adversarial perturbations: small changes in the input easily lead to misclassification. In this work, we propose an attack methodology not only for cases where the…

In this paper, we propose a method to design the training data that can support robust generalization of trained neural networks to unseen channels. The proposed design that improves the generalization is described and analysed. It avoids…

With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…