Related papers: Instance Optimal Decoding and the Restricted Isome…

In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…

Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the…

The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization…

This work gains a sharp sufficient condition on the block restricted isometry property for the recovery of sparse signal. Under the certain assumption, the signal with block structure can be stably recovered in the present of noisy case and…

In closed-loop distributed multi-sensor integrated sensing and communication (ISAC) systems, performance often hinges on transmitting high-dimensional sensor observations over rate-limited networks. In this paper, we first present a general…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…

The restricted isometry property (RIP) is a universal tool for data recovery. We explore the implication of the RIP in the framework of generalized sparsity and group measurements introduced in the Part I paper. It turns out that for a…

With the increasing adoption of Large Language Models (LLMs), more customization is needed to ensure privacy-preserving and safe generation. We address this objective from two critical aspects: unlearning of sensitive information and…

This paper considers a network where a node wishes to transmit a source message to a legitimate receiver in the presence of an eavesdropper. The transmitter secures its transmissions employing a sparse implementation of Random Linear…

Learning-based lossy image compression usually involves the joint optimization of rate-distortion performance. Most existing methods adopt spatially invariant bit length allocation and incorporate discrete entropy approximation to constrain…

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP)---i.e. they are approximately norm-preserving---the problem is known to contain no spurious local minima, so exact recovery…

Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. Such problem-dependent behavior is not captured by worst-case analyses and has accordingly inspired…

Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…

The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading…

The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…

This paper applies the recently axiomatized Optimum Information Principle (minimize the Kullback-Leibler information subject to all relevant information) to nonparametric density estimation, which provides a theoretical foundation as well…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…