Related papers: Optimal Shrinkage of Singular Values Under Random …

Deep neural networks can memorize corrupted labels, making data quality critical for model performance, yet real-world datasets are frequently compromised by both label noise and input noise. This paper proposes a mutual information-based…

We introduce a new model to study algorithm design under unreliable information, and apply this model for the problem of finding the uncorrupted maximum element of a list containing $n$ elements, among which are $k$ corrupted elements.…

Dealing with missing data in data analysis is inevitable. Although powerful imputation methods that address this problem exist, there is still much room for improvement. In this study, we examined single imputation based on deep…

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…

We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted sample points using Gaussian process regression. A heteroscedastic noise model is employed, in which additive…

Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…

We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…

Statistically consistent methods based on the noise transition matrix ($T$) offer a theoretically grounded solution to Learning with Noisy Labels (LNL), with guarantees of convergence to the optimal clean-data classifier. In practice,…

The inability of DNNs to explain their black-box behavior has led to a recent surge of explainability methods. However, there are growing concerns that these explainability methods are not robust and trustworthy. In this work, we perform…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…

The smallest singular value and condition number play important roles in numerical linear algebra and the analysis of algorithms. In numerical analysis with randomness, many previous works make Gaussian assumptions, which are not general…

Anomaly detection (AD) tasks have been solved using machine learning algorithms in various domains and applications. The great majority of these algorithms use normal data to train a residual-based model and assign anomaly scores to unseen…

In multimedia understanding tasks, corrupted samples pose a critical challenge, because when fed to machine learning models they lead to performance degradation. In the past, three groups of approaches have been proposed to handle noisy…

The randomized singular value decomposition (R-SVD) is a popular sketching-based algorithm for efficiently computing the partial SVD of a large matrix. When the matrix is low-rank, the R-SVD produces its partial SVD exactly; but when the…

The robustness to noise and outliers is an important issue in linear representation in real applications. We focus on the problem that samples are grossly corrupted, which is also the 'sample specific' corruptions problem. A reasonable…