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Unsupervised denoising is a crucial challenge in real-world imaging applications. Unsupervised deep-learning methods have demonstrated impressive performance on benchmarks based on synthetic noise. However, no metrics are available to…

This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals.…

We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

We propose an algorithm to solve optimization problems constrained by partial (ordinary) differential equations under uncertainty, with almost sure constraints on the state variable. To alleviate the computational burden of high-dimensional…

Graph convolutional networks (GCN) are viewed as one of the most popular representations among the variants of graph neural networks over graph data and have shown powerful performance in empirical experiments. That $\ell_2$-based graph…

We develop analytical and algorithmic techniques that enable efficient simulation of a broad class of noisy stabilizer circuits. We derive closed-form expressions of expectation values for tensor product of Paulis in circuits with…

We refine an old idea for performing fault-tolerant error correction in topological codes by simulating confining interactions between excitations. We implement confinement using an array of local classical processors that measure…

Designing robust algorithms capable of training accurate neural networks on uncurated datasets from the web has been the subject of much research as it reduces the need for time consuming human labor. The focus of many previous research…

Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…

In this paper, we tackle the problem of measuring similarity among graphs that represent real objects with noisy data. To account for noise, we relax the definition of similarity using the maximum weighted co-$k$-plex relaxation method,…

We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function and a (probably nonsmooth) convex function. The model…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…

Although large language models (LLMs) have achieved great success in vast real-world applications, their vulnerabilities towards noisy inputs have significantly limited their uses, especially in high-stake environments. In these contexts,…

Deep Metric Learning (DML) is a group of techniques that aim to measure the similarity between objects through the neural network. Although the number of DML methods has rapidly increased in recent years, most previous studies cannot…

As its availability and generality in online services, implicit feedback is more commonly used in recommender systems. However, implicit feedback usually presents noisy samples in real-world recommendation scenarios (such as misclicks or…

The Noise2Noise method allows for training machine learning-based denoisers with pairs of input and target images where both the input and target can be noisy. This removes the need for training with clean target images, which can be…