English
Related papers

Related papers: Regularization of the Kernel Matrix via Covariance…

200 papers

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…

Systems and Control · Computer Science 2016-10-25 Anna Marconato , Maarten Schoukens , Johan Schoukens

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

Machine Learning · Computer Science 2023-12-04 Franziska Nestler , Martin Stoll , Theresa Wagner

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

Functional Analysis · Mathematics 2017-12-15 Ingo Steinwart , Johanna F. Ziegel

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Machine Learning · Computer Science 2024-04-29 Theresa Wagner , Franziska Nestler , Martin Stoll

We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick…

Logic in Computer Science · Computer Science 2022-01-26 Luca Bortolussi , Giuseppe Maria Gallo , Jan Křetínský , Laura Nenzi

Multi-target linear shrinkage is an extension of the standard single-target linear shrinkage for covariance estimation. We combine several constant matrices - the targets - with the sample covariance matrix. We derive the oracle and a…

Statistics Theory · Mathematics 2025-03-13 Benoit Oriol

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we…

Machine Learning · Statistics 2014-12-01 Franz J. Király , Andreas Ziehe , Klaus-Robert Müller

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

Econometrics · Economics 2024-01-15 Chenlei Leng , Degui Li , Hanlin Shang , Yingcun Xia

The transcriptomics of cancer tumors are characterized with tens of thousands of gene expression features. Patient prognosis or tumor stage can be assessed by machine learning techniques like supervised classification tasks given a gene…

Machine Learning · Computer Science 2020-04-13 Martin Palazzo , Patricio Yankilevich , Pierre Beauseroy

This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…

Numerical Analysis · Computer Science 2014-11-04 Mostafa Rahmani , George Atia

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Machine Learning · Computer Science 2021-04-08 Danica J. Sutherland , Jeff Schneider

We consider shrinkage estimation of higher order Hilbert space valued Bochner integrals in a non-parametric setting. We propose estimators that shrink the $U$-statistic estimator of the Bochner integral towards a pre-specified target…

Statistics Theory · Mathematics 2022-07-22 Saiteja Utpala , Bharath K. Sriperumbudur

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

Data Analysis, Statistics and Probability · Physics 2012-09-19 N. D. Gagunashvili , M. Schmelling

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

Machine Learning · Computer Science 2019-08-06 Balázs Csanád Csáji , Krisztián Balázs Kis

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…

Methodology · Statistics 2022-02-08 Elias Raninen , David E. Tyler , Esa Ollila

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…

Machine Learning · Statistics 2023-03-16 Saad Hamid , Sebastian Schulze , Michael A. Osborne , Stephen J. Roberts

Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…

Machine Learning · Statistics 2019-11-22 Anderson Ara , Mateus Maia , Samuel Macêdo , Francisco Louzada

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Machine Learning · Computer Science 2013-05-23 Francis Bach

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

Computer Vision and Pattern Recognition · Computer Science 2020-03-30 Liangli Zhen , Dezhong Peng , Wei Wang , Xin Yao

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…

Methodology · Statistics 2024-11-11 Ziwei Su , Diego Klabjan