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

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…

For Euclidean space ($\ell_2$), there exists the powerful dimension reduction transform of Johnson and Lindenstrauss, with a host of known applications. Here, we consider the problem of dimension reduction for all $\ell_p$ spaces $1 \le p…

In learning problems, the noise inherent to the task at hand hinders the possibility to infer without a certain degree of uncertainty. Quantifying this uncertainty, regardless of its wide use, assumes high relevance for security-sensitive…

We present two fast constructions of weak*-copies of $\ell ^\infty$ in $H^{\infty}$ and show that such copies are necessarily weak*-complemented. Moreover, via a Paley-Wiener type of stability theorem for bases, a connection can be made in…

We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of…

We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…

We investigate compressed sensing (CS) techniques for reducing the number of measurements in photoacoustic tomography (PAT). High resolution imaging from CS data requires particular image reconstruction algorithms. The most established…

This paper studies the constrained/safe reinforcement learning (RL) problem with sparse indicator signals for constraint violations. We propose a model-based approach to enable RL agents to effectively explore the environment with unknown…

Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the output of…

Understanding the noise affecting a quantum device is of fundamental importance for scaling quantum technologies. A particularly important class of noise models is that of Pauli channels, as randomized compiling techniques can effectively…

The open source of large amounts of image data promotes the development of deep learning techniques. Along with this comes the privacy risk of these open-source image datasets being exploited by unauthorized third parties to train deep…

In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate…

Multi-modal Large Language Models (MLLMs) excel in vision-language tasks but remain vulnerable to visual adversarial perturbations that can induce hallucinations, manipulate responses, or bypass safety mechanisms. Existing methods seek to…

The robustness and anomaly detection capability of neural networks are crucial topics for their safe adoption in the real-world. Moreover, the over-parameterization of recent networks comes with high computational costs and raises questions…

In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of…

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have…