Related papers: Solving $\ell^p\!$-norm regularization with tensor…
Extreme learning machine (ELM) is an extremely fast learning method and has a powerful performance for pattern recognition tasks proven by enormous researches and engineers. However, its good generalization ability is built on large numbers…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…
The seminal paper of Daubechies, Defrise, DeMol made clear that $\ell^p$ spaces with $p\in [1,2)$ and $p$-powers of the corresponding norms are appropriate settings for dealing with reconstruction of sparse solutions of ill-posed problems…
Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approach exploits the local kernel theory which allows one to…
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…
This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…
Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
Recent empirical and theoretical studies have shown that many learning algorithms -- from linear regression to neural networks -- can have test performance that is non-monotonic in quantities such the sample size and model size. This…
Optimization methods that make use of derivatives of the objective function up to order $p > 2$ are called tensor methods. Among them, ones that minimize a regularized $p$th-order Taylor expansion at each step have been shown to possess…
Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a…
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…