Related papers: Data-Driven Linear Complexity Low-Rank Approximati…
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coefficients. Building upon the work of Kaarnioja, Kazashi, Kuo,…
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…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting…
Representation learning is an important step in the machine learning pipeline. Given the current biological sequencing data volume, learning an explicit representation is prohibitive due to the dimensionality of the resulting feature…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
The kernel interpolant in a reproducing kernel Hilbert space is optimal in the worst-case sense among all approximations of a function using the same set of function values. In this paper, we compare two search criteria to construct lattice…
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the…
Despite the recent deep learning (DL) revolution, kernel machines still remain powerful methods for action recognition. DL has brought the use of large datasets and this is typically a problem for kernel approaches, which are not scaling up…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks…
In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor…