Related papers: Efficient Reduced Basis Algorithm (ERBA) for kerne…
We study the problem of selecting the shape parameter in Radial Basis function (RBF) interpolation using leave-one-out-cross-validation (LOOCV). Since the classical LOOCV formula requires repeated solves with a dense $N \times N$ kernel…
We consider in this paper the formulation of approximate inference in Bayesian networks as a problem of exact inference on an approximate network that results from deleting edges (to reduce treewidth). We have shown in earlier work that…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…
Deep learning architectures have been widely fostered throughout the last years, being used in a wide range of applications, such as object recognition, image reconstruction, and signal processing. Nevertheless, such models suffer from a…
The artificial neural network shows powerful ability of inference, but it is still criticized for lack of interpretability and prerequisite needs of big dataset. This paper proposes the Rule-embedded Neural Network (ReNN) to overcome the…
Deep neural networks have become the dominant approach in natural language processing (NLP). However, in recent years, it has become apparent that there are shortcomings in systematicity that limit the performance and data efficiency of…
Previous work showed empirically that large neural networks can be significantly reduced in size while preserving their accuracy. Model compression became a central research topic, as it is crucial for deployment of neural networks on…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal.…
Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding…
Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly…
This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d-dimensional interpolation.…