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The Nystr\"{o}m method is an effective tool to generate low-rank approximations of large matrices, and it is particularly useful for kernel-based learning. To improve the standard Nystr\"{o}m approximation, ensemble Nystr\"{o}m algorithms…

Machine Learning · Statistics 2023-02-23 Keaton Hamm , Zhaoying Lu , Wenbo Ouyang , Hao Helen Zhang

Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional…

Machine Learning · Computer Science 2019-12-02 Luc Giffon , Stéphane Ayache , Thierry Artières , Hachem Kadri

Kernel ridge regression, in general, is expensive in memory allocation and computation time. This paper addresses low rank approximations and surrogates for kernel ridge regression, which bridge these difficulties. The fundamental…

Machine Learning · Statistics 2025-01-07 Paul Dommel

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Data Structures and Algorithms · Computer Science 2014-11-07 Andrej Gisbrecht , Frank-Michael Schleif

In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row…

Numerical Analysis · Mathematics 2018-03-15 Duan Chen , Wei Cai

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

Machine Learning · Statistics 2017-12-29 Fatemeh Sheikholeslami , Dimitris Berberidis , Georgios B. Giannakis

We study Nystr\"om type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that…

Machine Learning · Statistics 2016-03-18 Alessandro Rudi , Raffaello Camoriano , Lorenzo Rosasco

Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…

Machine Learning · Statistics 2024-01-26 Amirhesam Abedsoltan , Parthe Pandit , Luis Rademacher , Mikhail Belkin

Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…

Machine Learning · Computer Science 2014-04-02 Shusen Wang , Zhihua Zhang

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

Machine Learning · Computer Science 2022-06-22 Sattar Vakili , Jonathan Scarlett , Da-shan Shiu , Alberto Bernacchia

The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This…

Machine Learning · Computer Science 2024-12-04 José Ángel Martín-Baos , Ricardo García-Ródenas , Luis Rodriguez-Benitez , Michel Bierlaire

We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…

Machine Learning · Computer Science 2016-02-09 Weiran Wang

Kernel methods provide an elegant framework for developing nonlinear learning algorithms from simple linear methods. Though these methods have superior empirical performance in several real data applications, their usefulness is inhibited…

Machine Learning · Statistics 2021-05-20 Nicholas Sterge , Bharath Sriperumbudur

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…

Chemical Physics · Physics 2023-07-12 Stefan Blücher , Klaus-Robert Müller , Stefan Chmiela

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

Machine Learning · Computer Science 2020-10-16 Fanghui Liu , Xiaolin Huang , Chen Gong , Jie Yang , Li Li

Kernel methods are used frequently in various applications of machine learning. For large-scale high dimensional applications, the success of kernel methods hinges on the ability to operate certain large dense kernel matrix K. An enormous…

Numerical Analysis · Mathematics 2021-12-30 Difeng Cai , James Nagy , Yuanzhe Xi

Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…

Machine Learning · Computer Science 2020-02-21 Michaël Fanuel , Joachim Schreurs , Johan A. K. Suykens

Low-rank matrix decomposition has gained great popularity recently in scaling up kernel methods to large amounts of data. However, some limitations could prevent them from working effectively in certain domains. For example, many existing…

Machine Learning · Computer Science 2012-08-27 Kai Zhang , Liang Lan , Jun Liu , andreas Rauber , Fabian Moerchen

The Nystr\"om method is one of the most popular techniques for improving the scalability of kernel methods. However, it has not yet been derived for kernel PCA in line with classical PCA. In this paper we derive kernel PCA with the…

Machine Learning · Statistics 2022-08-22 Fredrik Hallgren

The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected…

Machine Learning · Statistics 2016-12-21 Farhad Pourkamali-Anaraki , Stephen Becker