English
Related papers

Related papers: Fast deterministic approximation of symmetric inde…

200 papers

Transformers are expensive to train due to the quadratic time and space complexity in the self-attention mechanism. On the other hand, although kernel machines suffer from the same computation bottleneck in pairwise dot products, several…

Machine Learning · Computer Science 2021-11-02 Yifan Chen , Qi Zeng , Heng Ji , Yun Yang

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

Optimization and Control · Mathematics 2020-11-20 Adam J. Thorpe , Kendric R. Ortiz , Meeko M. K. Oishi

A general, {\em rectangular} kernel matrix may be defined as $K_{ij} = \kappa(x_i,y_j)$ where $\kappa(x,y)$ is a kernel function and where $X=\{x_i\}_{i=1}^m$ and $Y=\{y_i\}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank…

Numerical Analysis · Mathematics 2023-06-30 Difeng Cai , Edmond Chow , Yuanzhe Xi

In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields…

Machine Learning · Computer Science 2025-09-19 Tizian Wenzel , Gabriele Santin , Bernard Haasdonk

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

Machine Learning · Computer Science 2012-02-20 Nima Reyhani , Hideitsu Hino , Ricardo Vigario

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

Quantum Physics · Physics 2022-11-29 Daniel T. Chang

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Machine Learning · Computer Science 2020-02-17 Mert Al , Zejiang Hou , Sun-Yuan Kung

We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to large-scale data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP).…

Machine Learning · Statistics 2023-02-09 Veit Wild , Motonobu Kanagawa , Dino Sejdinovic

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Machine Learning · Statistics 2015-03-03 E. Cruz Cortés , C. Scott

This paper proposes K-NRM, a kernel based neural model for document ranking. Given a query and a set of documents, K-NRM uses a translation matrix that models word-level similarities via word embeddings, a new kernel-pooling technique that…

Information Retrieval · Computer Science 2017-06-22 Chenyan Xiong , Zhuyun Dai , Jamie Callan , Zhiyuan Liu , Russell Power

The spectrum of a kernel matrix significantly depends on the parameter values of the kernel function used to define the kernel matrix. This makes it challenging to design a preconditioner for a regularized kernel matrix that is robust…

Numerical Analysis · Mathematics 2024-04-10 Shifan Zhao , Tianshi Xu , Hua Huang , Edmond Chow , Yuanzhe Xi

Machine learning (ML) models, such as SVM, for tasks like classification and clustering of sequences, require a definition of distance/similarity between pairs of sequences. Several methods have been proposed to compute the similarity…

Machine Learning · Computer Science 2022-09-13 Sarwan Ali , Bikram Sahoo , Muhammad Asad Khan , Alexander Zelikovsky , Imdad Ullah Khan , Murray Patterson

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…

Machine Learning · Statistics 2025-01-17 Yifei Xiong , Xiliang Yang , Sanguo Zhang , Zhijian He

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

Machine Learning · Statistics 2018-06-06 Hiroaki Sasaki , Aapo Hyvärinen

This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…

Optimization and Control · Mathematics 2024-05-28 Peter Richtárik , Abdurakhmon Sadiev , Yury Demidovich

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…

Machine Learning · Computer Science 2014-05-28 Omid Aghazadeh , Stefan Carlsson

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

Numerical Analysis · Mathematics 2026-03-09 Marian Klink , Tobias Ehring , Robin Herkert , Robin Lautenschlager , Dominik Göddeke , Bernard Haasdonk

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…

Machine Learning · Statistics 2025-06-23 Mike Nguyen , Nicole Mücke

Recently, the computer vision and machine learning community has been in favor of feature extraction pipelines that rely on a coding step followed by a linear classifier, due to their overall simplicity, well understood properties of linear…

Machine Learning · Computer Science 2013-04-17 Oriol Vinyals , Yangqing Jia , Trevor Darrell

The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…

Numerical Analysis · Mathematics 2024-04-24 Alberto Bucci , Leonardo Robol