Neural network learns kernel functions for survival analysis and prediction intervals.
problem Predicting survival times for individuals based on similar training subjects.
method Develops a neural network framework to learn kernel functions for kernel survival analysis and uses these to construct valid prediction intervals.
result Neural network survival estimators are competitive with existing methods and provide valid prediction intervals.
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on the kernel matrix defines an explicit nonlinear mapping of the input data represen…
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
Paper introduces RKHM and KME for richer data analysis.
problem Lack of rich data structures in kernel methods.
method Proposes RKHM and KME for functional data analysis.
result RKHM captures structural properties in functional data.
Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
problem Understanding the Gaussian RBF kernel in machine learning and SVMs.
method Using Fock space and Segal-Bargmann theories in complex analysis.
result Proves connections between Gaussian RBF kernels and quantum mechanics operators.
A new method generalizing subspace learning for improved classification.
problem Improving classification accuracy using subspace learning methods.
method Roweis Discriminant Analysis (RDA) which generalizes PCA, SPCA, and FDA.
result RDA and kernel RDA improve classification accuracy on benchmark datasets.
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that …
Sentiment analysis consists of evaluating opinions or statements from the analysis of text. Among the methods used to estimate the degree in which a text expresses a given sentiment, are those based on Gaussian Processes. However, traditional Gaussian Processes methods use a predefined kernel with hyperparameters that …
Paper introduces RKHM for more explicit variable structures analysis.
problem Explicitly analyzing structures among variables.
method Orthonormal systems in Hilbert C∗-modules, RKHM. result Theoretical and practical procedures for RKHM orthonormalization.
New kernel method for shape classification on Kendall shape space.
problem Classification of shapes on non-Euclidean Kendall shape space.
method Extrinsic Veronese Whitney Gaussian kernel for KRRC on Σ2k. result KRRC classifier performs well on real Kendall shape data.
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel…
Survival kernets scale deep kernel survival analysis to large datasets with interpretability and theoretical guarantees.
problem Scalable and interpretable deep kernel survival analysis for large datasets.
method Survival kernets use kernel netting for training set compression and XGBoost for warm-starting neural architecture search.
result Survival kernets achieve optimal time-dependent concordance index on various survival analysis datasets.
Signature kernel handles sequential data with theoretical and practical advantages.
problem Handling sequential data efficiently and accurately.
method Positive definite kernel based on stochastic analysis with efficient computation.
result Strong empirical performance and theoretical guarantees.
New theoretical tools simplify kernel-based tests analysis.
problem Asymptotic behavior of kernel-based tests in various scenarios.
method Avoids complex expansions and limit theorems, works directly with Hilbert spaces random functionals.
result Framework leads to simpler analysis with minimal regularity conditions.
RKUM is an R package for robust kernel-based unsupervised methods.
problem Robust analysis under contaminated or noisy data conditions.
method Robust kernel covariance and cross-covariance operators using generalized loss functions.
result RKUM reduces sensitivity to contamination and effectively identifies outliers.
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…
Proposes KMvDA for object recognition from multi-view data.
problem Recognizing objects from different views, even when views are heterogeneous.
method Introduces kernel multi-view discriminant analysis (KMvDA) and uses random Fourier features (RFF) for large-scale learning.
result KMvDA and RFF approximation improve object recognition from multi-view data.
Generalizes neural tangent kernel analysis for two-layer networks with noise and regularization.
problem Limitations of NTK analysis in deep learning practice.
method Generalized NTK analysis for two-layer neural networks with weight decay and gradient noise.
result Noisy gradient descent with weight decay exhibits 'kernel-like' behavior and converges linearly.
Survey on manifold ends with new heat kernel estimates.
problem Analyzing geometric properties on manifolds with ends.
method Constructing manifolds with ends and analyzing their heat kernel estimates.
result Found manifolds with ends that have different heat kernel estimates.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to …
The study extends kernel universality to Riemannian symmetric spaces.
problem Understanding kernel universality in non-Euclidean domains.
method Harmonic analysis on Riemannian symmetric spaces.
result Proves universality of recent kernels on Riemannian symmetric spaces.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It…
Two-layer neural networks learn efficiently using kernel methods in mean-field analysis.
problem Feature learning ability of two-layer neural networks in the mean-field regime.
method Mean-field analysis through kernel methods, focusing on dynamics of the first layer's kernel.
result Two-layer neural networks can learn a union of multiple reproducing kernel Hilbert spaces more efficiently than kernel methods.
Criterion extends identifiability for continuous mixtures of kernels.
problem Identify continuous mixtures of kernels.
method Generating-function accessibility criterion based on moment-generating functions or Laplace transforms.
result Criterion applies to mixtures of discrete and continuous variables.
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
Study spectral properties of graph Laplacian for manifold data.
problem Understanding spectral properties of graph Laplacian for manifold data.
method Non-asymptotic error bounds on spectral properties of empirical graph Laplacian.
result Eigenvalues and eigenspaces of empirical graph Laplacian are close to Laplace-Beltrami operator of manifold.
Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant outliers is an essential and challenging issue for imaging genetics and multiple source…
Kernel and Multiple Kernel Canonical Correlation Analysis (CCA) are employed to classify schizophrenic and healthy patients based on their SNPs, DNA Methylation and fMRI data. Kernel and Multiple Kernel CCA are popular methods for finding nonlinear correlations between high-dimensional datasets. Data was gathered from …
In genome-wide interaction studies, to detect gene-gene interactions, most methods are divided into two folds: single nucleotide polymorphisms (SNP) based and gene-based methods. Basically, the methods based on the gene are more effective than the methods based on a single SNP. Recent years, while the kernel canonical …
Enhanced kernel ridgeless regression improves performance with LAB RBF kernels.
problem Lack of flexibility in kernel ridgeless regression.
method Locally-Adaptive-Bandwidths (LAB) RBF kernels and kernel learning techniques.
result Functions learned from LAB RBF kernels belong to an integral space of RKHSs, demonstrating robust generalization.
Paper develops a dual formulation for PCA in Hilbert spaces.
problem Characterizing probabilistic PCA in Hilbert spaces.
method Dual formulation for probabilistic PCA in Hilbert spaces.
result Generative framework for kernel methods developed.
A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this e…
Bayesian model merges multi-view latent models and kernel methods.
problem Handling high-dimensionality and non-linear issues in multi-view data.
method Combines probabilistic factor analysis with kernelized observations.
result Compact solutions for kernelized observations and feature selection.
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …
New PCA method detects faults using occupation kernels.
problem Fault detection in dynamical systems.
method Occupation kernel PCA for irregularly sampled data.
result Validation of reconstruction error approach for fault detection.
Kernel testing compares cell states in single-cell data.
problem Comparing non-linear cell states in single-cell data.
method Kernel-based testing framework for non-linear distribution comparison.
result Identifies subtle population variations in cell states.
PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
Study of regularized least squares in RKKS with indefinite kernels.
problem Asymptotic properties of regularized least squares with indefinite kernels in RKKS.
method Introducing a bounded hyper-sphere constraint, theoretical demonstration of globally optimal solution, modified error decomposition techniques, matrix perturbation theory.
result Derivation of learning rates in RKKS, same as RKHS under certain conditions.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
problem Privacy-preserving data collaboration with reduced reconstruction risk.
method Formulates linear kernel integration, kernelizes it, and introduces graph regularization and centering constraints.
result NKI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction.
Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations between datasets. Despite their wide usage, they have one common limitation that…
Unified analysis of kernel-based and locally adaptive bandit optimization methods.
problem Performance of bandit optimization algorithms in RKHS functions.
method Investigates the relationship between kernel regularity and algorithmic performance, characterizing spectral properties of various kernels.
result Unified framework for analyzing kernel-based and locally adaptive bandit algorithms, deriving explicit regret bounds.
The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corres…
Kernelmethods library simplifies kernel-based ML in Python.
problem Lack of a well-defined Python library for kernel-based ML.
method Develops a Python library that supports various kernel types and customizations.
result Enables efficient, modular, and interoperable kernel-based operations.
Kernelized cumulants improve statistical analysis in high-dimensional spaces.
problem Statistical analysis in high-dimensional spaces with low variance estimators.
method Extending cumulants to RKHS using tensor algebra and kernel trick.
result Kernelized cumulants provide new all-purpose statistics with computational tractability.
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of data points. We provide a new analysis of a class of approximate kernel methods…
Paper extends RPD for better handling multiple modalities and non-convexity.
problem Handling multiple modalities and non-convexity in data clouds.
method Computes RPD in a reproducing kernel Hilbert space using kernel principal component analysis.
result The method outperforms RPD and is comparable to other models on benchmark datasets.