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.
This paper uses machine learning to select kernels for machine learning models on various devices.
problem Traditional kernel auto-tuning is limited for machine learning research with changing network topologies and hyperparameters.
method Combines auto-tuning and machine learning to select kernels for SYCL on various devices.
result Initial results show high performance kernel selection with little developer effort.
This note offers a theoretical explanation for the success of classical kernels in machine learning.
problem Understanding why classical kernels like Gaussian RBF and Sobolev kernels are often successful in machine learning.
method Analyzes the connection between extension theorems and universal consistency in the context of kernel methods.
result Provides a theoretical explanation for the empirical success of classical kernels.
Online machine learns from signals robustly using consensus optimization.
problem Signal classification in online settings.
method Reproducing kernel Hilbert space with consensus optimization.
result Robust signal classification achieved.
This work introduces a new quantum kernel, quantum tangent kernel, for improved performance.
problem Improving quantum machine learning performance beyond conventional methods.
method Developed a deep parameterized quantum circuit and used first-order expansion for training.
result The quantum tangent kernel outperforms conventional quantum kernel methods for ansatz-generated datasets.
Optimizes kernel machines using deep learning for efficiency and end-to-end learning.
problem Limited training data and lack of explicit feature sources.
method DKMO (Deep Kernel Machine Optimization) framework using Nystrom kernel approximations and deep learning.
result Improved training convergence and effectiveness over conventional model inferencing techniques.
New approach to learning kernels from data using AIT principles.
problem Learning kernels from data in machine learning.
method Sparse Kernel Flows method based on AIT principles.
result Sparse Kernel Flows aligns with MDL principle and offers a robust theoretical foundation.
Quantum kernel machines need to use more complex kernels to fully exploit their potential.
problem Current quantum kernels struggle with complex learning tasks due to limited degrees of freedom.
method Propose using operator-valued kernels and C∗-algebraic representations to enhance quantum kernels. result Quantum operator-valued kernels can reveal structural dependencies that scalar-valued kernels miss.
Unified framework combines trace-induced quantum kernels for improved machine learning models.
problem Improving performance of quantum machine learning models using trace-induced kernels.
method Developed a unified framework combining various trace-induced quantum kernels, including global fidelity and local projected kernels, as Lego kernels.
result Local projected kernels can achieve comparable performance to global fidelity kernels with fewer quantum resources.
Paper defines kernels for fuzzy sets, useful in machine learning.
problem Uncertainty in data with fuzzy set membership.
method Defined cross product, intersection, non-singleton, and distance-based kernels.
result Kernels improve machine learning tasks with fuzzy data.
New kernels use sliced Wasserstein for better probability distribution learning.
problem Learning from probability distributions efficiently.
method Sliced Wasserstein kernels based on optimal transport distances.
result Improved performance in various machine learning tasks.
Kernel for STL formulae enables machine learning in temporal logic.
problem Lack of a kernel for STL formulae.
method Define a kernel for STL formulae and embed them into a Hilbert space.
result Kernel-based machine learning algorithms can now be applied to STL formulae.
Quantum machine learning for 2D classification tasks using optimized feature maps.
problem Classifying data points in finite feature space with quantum machine learning.
method Optimized quantum feature maps and classical model training.
result Exponentially better scaling of deployed kernels in qubit number.
Machine learning with kernels for portfolio valuation and risk management.
problem Dynamic portfolio valuation and risk management in finance.
method Machine learning with kernels to learn the dynamic value process of a portfolio from cumulative cash flow data.
result Asymptotic consistency and finite sample error bounds demonstrated for finance applications.
Neural networks can learn kernel machines with a data-dependent kernel.
problem Can neural networks in the rich feature learning regime learn a kernel machine?
method Demonstrated silent alignment effect in neural networks, showing they can learn a kernel machine with a data-dependent kernel.
result Neural networks in the rich feature learning regime can learn a kernel machine with a data-dependent kernel due to silent alignment.
Deep networks are mathematically equivalent to kernel machines learned by gradient descent.
problem Understanding the learned representations of deep learning models.
method Using gradient descent to learn deep networks, showing they are equivalent to kernel machines.
result Deep network weights are a superposition of training examples, revealing the learned function.
Study on kernel methods in large-scale machine learning problems.
problem Large-scale machine learning with many interacting variables.
method Mean field limit analysis of kernels and their Hilbert spaces.
result Mean field convergence of empirical and infinite-sample solutions.
Preconditioned conjugate gradients improve kernel machine scalability.
problem Poor convergence of conjugate gradients on kernel matrices.
method Developed preconditioned conjugate gradients for kernel machines.
result Preconditioned conjugate gradients outperform state-of-the-art approximations.
Kernel for multi-parameter persistent homology connects TDA with ML.
problem Connecting persistent homology with machine learning for multivariate data.
method Integrating a one-parameter kernel weighted along straight lines.
result Stable and efficiently computable kernel for multi-parameter persistence.
Quantum models are rephrased as kernel methods, improving performance.
problem Improving quantum machine learning models by encoding data into quantum states.
method Rephrasing quantum models as kernel methods and using support vector machines.
result Kernel-based training finds better quantum models than variational circuit training.
Improved deep kernel machine achieves 94.5% test accuracy on CIFAR-10.
problem Achieving high accuracy on complex tasks like image classification.
method Stochastic kernel regularisation to add noise to learned Gram matrices.
result 94.5% test accuracy on CIFAR-10.
New method preserves privacy while improving machine learning accuracy.
problem Privacy-preserving machine learning for daily data.
method Compressive Privacy and multi-kernel method.
result Improved utility classification accuracy with privacy preservation.
Transformers are explained as infinite-dimensional kernel machines.
problem Understanding the mechanics of Transformers in AI.
method Characterized Transformers' attention mechanism as a kernel learning method on Banach spaces.
result Transformer's kernel has infinite feature dimension and can learn any binary non-Mercer reproducing kernel Banach space pair.
Random Machines improves SVM performance with free kernel choice.
problem Efficiency and accuracy in solving classification and regression problems.
method Bagged-weighted support vector model with free kernel choice.
result Improved accuracy and reduced computational time.
Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature space. We argue that linear classification in the feature space of kernels comm…
This study simplifies learning kernel matrices for SVMs.
problem Learning distances between unlabeled pairs in partially labeled datasets.
method Semidefinite programming to optimize kernel matrices.
result Improved understanding of kernel matrix learning.
Proposes learning manifold implicitly via heat kernel.
problem Direct manifold learning methods lack flexibility for down-stream applications.
method Implicit manifold learning using heat kernel.
result Framework achieves state-of-the-art results for data generation and Bayesian inference.
New q-Hermite kernel improves SVM performance without scaling.
problem Improving SVM performance through novel kernel design.
method Introducing q-Hermite kernel based on q-Hermite I polynomials. result The q-Hermite kernel achieves competitive performance compared to classical kernels.
New algorithm speeds up polynomial kernel approximations.
problem Efficiently approximating polynomial kernels of high degree.
method Oblivious sketching combined with novel sampling.
result Polynomial factor slowdown removed in running time.
Kempe discusses NTK approach to machine learning problems.
problem Generally unsolvable machine learning problems.
method NTK approach focusing on kernel formulations.
result Practical applications like data distillation and adversarial robustness.
Proposes a new kernel technique for tensor data in SVM.
problem Handling tensorial data in machine learning.
method Kernelized support tensor train machine for image classification.
result Tensorizes the standard SVM on its input structure and kernel mapping scheme.
Kernel methods linked to feature subspaces and maximal correlation kernels.
problem Understanding kernel methods and their relationship to feature extraction.
method Established a correspondence between feature subspaces and kernels, introduced maximal correlation kernels, and demonstrated their optimality.
result Kernel SVM on maximal correlation kernel achieves minimum prediction error.
The paper explores how predictive distributions are integrated with kernel methods in machine learning.
problem Integrating predictive distributions with kernel methods in machine learning.
method Combining predictive distributions with kernel methods.
result New insights into how predictive distributions can be effectively used with kernel methods.
A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.
problem How to provide principled uncertainty estimates for tensor network kernel machines.
method Employing a linearized Laplace approximation for Bayesian inference.
result Consistently matches or surpasses Gaussian Processes and BNNs across diverse UCI regression benchmarks.
Adaptive kernels from neural networks improve model performance.
problem Improving neural network performance through adaptive kernels.
method Deriving adaptive kernels from infinite-width neural networks using feature learning and gradient flow training.
result Adaptive kernels achieve lower test loss compared to traditional kernels.
SFM uses linear models in extended feature spaces to avoid kernel issues.
problem Difficulty in interpreting SVM solutions and limitations of single kernel types.
method Support Feature Machines (SFM) use linear models in extended feature spaces.
result SFM provides at least as good results as kernel-based SVMs without interpretation, scaling, and convergence issues.
Paper analyzes localized SVMs for robustness and consistency.
problem Handling large datasets efficiently and robustly.
method Localized support vector machines (SVMs) for non-parametric learning.
result Locally learnt kernel methods are universal consistent and robust.
Quantum neural tangent kernels help understand variational quantum circuits in machine learning.
problem Designing and predicting performance of variational quantum circuits.
method Using quantum neural tangent kernels and dynamical equations for loss functions.
result Analytical solutions for training dynamics in variational quantum circuits.
Kernel methods' derivatives make complex models more interpretable.
problem Interpreting complex kernel models.
method Deriving kernel functions' derivatives and applying them to various kernel methods.
result Derivatives of kernel functions can be computed and applied to improve model interpretation.
Bayesian nonparametric kernel-learning (BaNK) scales kernel methods to large datasets.
problem Limited flexibility and scalability of kernel methods for large datasets.
method Bayesian nonparametric approach to learn kernels from data.
result BaNK outperforms other scalable approaches for kernel learning.
New method speeds up kernel-based machine learning for force field reconstruction.
problem Scalability issues in kernel-based machine learning for force field reconstruction.
method Nyström-type methods to construct preconditioners based on low-rank approximations of the kernel matrix.
result Effective preconditioners lead to super-linear convergence in kernel-based machine learning.
DEK combines deep learning and kernel methods for better data mapping.
problem Improving data mapping for better performance in various machine learning tasks.
method A learnable kernel represented by a deep architecture explicitly trained to optimize feature space.
result DEK outperforms typical machine learning methods in multiple tasks.
TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection
problem Kernel learning and model selection
method GPU acceleration
result Competitive predictive performance with speedups
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on C∗-algebra. result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
ROCK method generalizes MOCK for learning dynamical systems efficiently.
problem Learning dynamical systems from data efficiently.
method Variational formulation in Reproducing Kernel Hilbert Spaces.
result ROCK method is more computationally efficient and performs better on benchmarks.
Nystrom method approximates GMM kernel for large datasets.
problem Efficiently computing GMM kernel for large-scale datasets.
method Apply Nystrom method to approximate GMM kernel.
result GMM-NYS approximates GMM kernel with comparable accuracy using fewer samples.
New algorithm learns kernels for multi-task learning.
problem Improving performance in multi-task learning scenarios.
method Support Vector Machine-regularized model with neighborhood kernels.
result Consistently outperforms traditional kernel learning methods.
Enhances machine learning for complex systems by embedding transition manifolds.
problem Identifying low-dimensional dynamics in high-dimensional multiscale systems.
method Kernel embeddings of transition manifolds in reproducing kernel Hilbert spaces.
result Robust and more efficient algorithm for identifying reaction coordinates.