Related papers: Constructing test instances for Basis Pursuit Deno…
Variational sparsity regularization based on $\ell^1$-norms and other nonlinear functionals has gained enormous attention recently, both with respect to its applications and its mathematical analysis. A focus in regularization theory has…
Classification is a fundamental problem in machine learning and data mining. During the past decades, numerous classification methods have been presented based on different principles. However, most existing classifiers cast the…
We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data…
Few-shot learning has attracted intensive research attention in recent years. Many methods have been proposed to generalize a model learned from provided base classes to novel classes, but no previous work studies how to select base…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
Denoising has to do with estimating a signal $x_0$ from its noisy observations $y=x_0+z$. In this paper, we focus on the "structured denoising problem", where the signal $x_0$ possesses a certain structure and $z$ has independent normally…
Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising…
The drastic increase of data quantity often brings the severe decrease of data quality, such as incorrect label annotations, which poses a great challenge for robustly training Deep Neural Networks (DNNs). Existing learning \mbox{methods}…
This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising…
Label noise will degenerate the performance of deep learning algorithms because deep neural networks easily overfit label errors. Let X and Y denote the instance and clean label, respectively. When Y is a cause of X, according to which many…
Though achieving excellent performance in some cases, current unsupervised learning methods for single image denoising usually have constraints in applications. In this paper, we propose a new approach which is more general and applicable…
We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. these problems are motivated by the lasso framework and have applications in machine learning and computer…
With this paper, we contribute to the growing research area of feature-based analysis of bio-inspired computing. In this research area, problem instances are classified according to different features of the underlying problem in terms of…
Many of the core disciplines of artificial intelligence have sets of standard benchmark problems well known and widely used by the community when developing new algorithms. Constraint programming and automated planning are examples of these…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…
This paper focuses on the estimation of low-complexity signals when they are observed through $M$ uniformly quantized compressive observations. Among such signals, we consider 1-D sparse vectors, low-rank matrices, or compressible signals…