Paper analyzes learning rates for SVM with Gaussian kernels.
problem Optimizing learning rates for binary classification.
method Refined error analysis for SVM with Gaussian kernel and convex loss.
result SVM with Gaussian kernel can achieve optimal learning rates under certain conditions.
Adapts exponential weights algorithm for kernel losses in online learning.
problem Online learning with kernel losses.
method Adapts exponential weights algorithm for kernel losses.
result Sharp bounds on regret for different kernel eigendecay conditions.
Improved robustness in kernel-based regression via novel loss function and IRLS.
problem Noise sensitivity in kernel-based regression methods.
method Proposed ℓs-loss function and iteratively reweighted least squares (IRLS) optimization. result Improved noise robustness in kernel-based regression methods.
Paper investigates robustness of RPL methods using kernels.
problem Robustness of regularized pairwise learning methods.
method Investigates RPL methods based on kernels for robustness.
result RPL methods can be statistically robust with proper loss and kernel choices.
Paper develops a duality approach for robust loss functions in infinite-dimensional RKHSs.
problem Robustness issues in infinite-dimensional RKHSs with operator-valued kernels.
method Develops a duality approach to solve OVK machines for various loss functions.
result Empirical improvements and theoretical stability analysis for robust structured data applications.
A new kernel risk-sensitive loss improves adaptive filtering robustness and speed.
problem Improving adaptive filtering performance in non-Gaussian environments.
method Introducing kernel risk-sensitive loss (KRSL) and developing MKRSL algorithm.
result MKRSL achieves faster convergence and higher accuracy with robustness to outliers.
Deep neural networks for structured prediction using kernel-induced losses.
problem Structured prediction tasks for images and texts.
method Designing a novel family of deep neural architectures that predict in a finite-dimensional subspace derived from the kernel-induced loss.
result Gradient descent algorithms can be used for structured prediction with deep neural networks.
A new algorithm tackles adversarial linear contextual bandits using kernelized loss functions.
problem Online learning in adversarial linear contextual bandits with flexible loss functions.
method Proposes a computationally efficient algorithm using an optimistically biased estimator for reproducing kernel Hilbert space loss functions.
result Achieves near-optimal regret guarantees under polynomial and exponential eigendecay assumptions.
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
Kernel method outperforms deep neural networks in speech enhancement.
problem Improving single-channel speech enhancement performance.
method Kernel regression with an exponential power kernel and EigenPro iterative method.
result Kernel method consistently outperforms deep neural networks in speech enhancement.
New method reduces second-order KOCO complexity with adaptive sketching.
problem Efficiently solving kernel online convex optimization problems with strong curvature.
method Kernel Online Newton Step (KONS) with adaptive matrix sketching.
result Achieves O(dextefflogT) regret with reduced space and time complexity. The study analyzes spectral algorithms for kernel methods and derives generalization error.
problem Estimating generalization error of spectral algorithms for kernel methods.
method Considered spectral algorithms including KRR and GD, derived generalization error as a functional of learning profile.
result Showed the loss localizes on certain spectral scales and conjectured universality of the loss for noisy observations.
Optimizes learning rates for kernel-based expectile regression.
problem Estimating conditional expectiles efficiently.
method Support vector machine type approach using Gaussian RBF kernels.
result Learning rates are minimax optimal with a logarithmic factor.
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.
Unified analysis of kernel-based methods under covariate shift.
problem Covariate shift in learning problems.
method Unified analysis of nonparametric methods in RKHS.
result Sharp convergence rates for general loss functions.
New method uses Kernel Flows to improve neural network training without changing structure.
problem Improving neural network training without altering structure or output classifier.
method Combines KFs with a classical output loss to aggregate a subset of KF losses.
result Reduced test errors, decreased generalization gaps, increased robustness to distribution shift.
This work analyzes when contrastive models are close to PCA or kernel methods.
problem Understanding when contrastive models are equivalent to kernel methods or PCA.
method Analyzing the training dynamics of two-layer contrastive models with non-linear activation.
result Wide contrastive models with cosine similarity based losses are close to PCA.
This paper speeds up kernel methods using sparsified Gaussian sketches.
problem Kernel methods' computational limitations.
method Sparsified Gaussian sketches for kernel methods.
result Efficient time and space savings for kernel methods.
We discover scaling laws for kernel regression loss under various learning rate schedules.
problem Understanding loss dynamics and learning rate schedules in kernel regression.
method Theoretical analysis of stochastic gradient descent on a power-law kernel regression model.
result Established a Functional Scaling Law (FSL) capturing the full loss trajectory under arbitrary learning rate schedules.
Robust methods for kernel CO and CCO improve unsupervised learning.
problem Sensitivity of kernel CO and CCO to contaminated data.
method Robust kernel CO and CCO based on generalized loss function, influence function, and visualization method.
result Robust kernel CCA shows superior performance over classical methods.
Proposes a Gradient Boosting method for learning adaptive kernel functions.
problem Learning a versatile ensemble of kernel functions for better performance.
method Approximates kernel functions as a weighted sum of Random Fourier Features and optimizes their barycenter at each iteration.
result Shows improved performance compared to Boosting-based and kernel-learning methods.
Exponential testing error reduction with stochastic gradient methods under low-noise conditions.
problem Binary classification with positive definite kernels and square loss.
method Stochastic gradient methods under low-noise conditions.
result Testing error converges exponentially fast, while testing loss converges slowly.
Paper connects risk consistency to L_p consistency for broader loss functions.
problem Establishing risk consistency for a wider class of loss functions.
method Analyzes the connection between risk consistency and L_p-consistency for various loss functions.
result Shifted loss functions do not reduce assumptions as much as other results.
Paper introduces a new error measure for robust learning.
problem Developing robust learning algorithms.
method Defined and applied the kernel mean-p power error (KMPE) to ELM and PCA.
result KMPE-based algorithms outperform existing methods.
Robust kernel CCA method detects outliers and improves performance.
problem Kernel CO and CCO sensitivity to contaminated data.
method Proposed robust kernel CO and CCO, derived IF for CCA, robust kernel CCA method.
result Robust kernel CCA method performs better than standard kernel CCA for ideal and contaminated data.
Proposes a robust framework for multiclass classification.
problem General multiclass classification with adversarial robustness.
method Dual formulation as convex optimization with adversarial surrogate loss.
result Competitive performance in multiclass classification problems.
A novel dictionary-based approach for predicting functions.
problem Functional-output regression with non-orthogonal dictionaries.
method Projection learning (PL) with reproducing kernel Hilbert spaces (KPL).
result KPL offers a flexible and computationally efficient solution.
New approach estimates personalized treatment effects using surrogate losses.
problem Estimating personalized treatment effects with binary outcomes and limited data.
method Proposes surrogate loss functions that incorporate both treatment and control data.
result Minimax support vector machine formulation yields tighter bounds.
Paper establishes a generalization bound for gradient flow using a data-dependent kernel.
problem Understanding the generalization properties of gradient-based optimization methods.
method Establishes a generalization bound for gradient flow through a data-dependent kernel called the loss path kernel (LPK).
result The LPK captures the entire training trajectory and leads to tighter generalization guarantees.
Paper introduces robust distribution regression using kernel methods.
problem Distribution regression from probability measures to real-valued responses.
method Introduces a robust loss function lσ and a windowing function V for two-stage sampling problems. result Shows improved learning rates and robustness with the robust distribution regression (RDR) scheme.
DGKIP extends KIP for dataset distillation without bi-level optimization.
problem Efficiently distill datasets for various loss functions.
method Leverages duality theory to avoid bi-level optimization.
result DGKIP supports a wider range of loss functions.
Paper introduces MRCs that minimize worst-case 0-1 loss, providing tight performance guarantees.
problem Minimizing worst-case 0-1 loss in classification.
method MRCs that minimize worst-case 0-1 loss with uncertainty sets of distributions.
result MRCs provide tight performance guarantees and are strongly universally consistent.
Novel method learns memory kernels in Langevin equations.
problem Estimating memory kernels in Langevin equations.
method Regularized Prony method for correlation functions, followed by regression over Sobolev norm-based loss function with RKHS regularization.
result Method outperforms other regression estimators in exponentially weighted L^2 space.
Neural networks and linear systems linked, revealing training loss and kernel limitations.
problem Exploring the training loss and limitations of neural networks and their kernels.
method Drawing connections between neural networks and under-determined linear systems, providing lower bounds, and analyzing gradient descent.
result Zero training loss achievable for neural networks under certain conditions, but not for ReLU kernels.
Kernel Quantization improves CNN compression without sacrificing performance.
problem Efficiently compressing CNN models without significant performance loss.
method Quantizes convolution kernels as the unit, learning a codebook for low-bit indexes.
result Significant compression ratio achieved with minimal accuracy loss.
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have demonstrated their usefulness in many complicated real-life problems. During the last…
Develops a new framework for robust regression with EGM.
problem Addressing robust regression with heavy-tailed noise or outliers.
method Empirical gain maximization (EGM) to approximate noise density.
result Unified analysis of robust regression approaches.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
Paper introduces MKL-L0/1-SVM for SVM with (0,1) loss.
problem Optimization of SVM with (0,1) loss function. method MKL framework combined with ADMM algorithm for solving the optimization problem.
result Performance of MKL-L0/1-SVM comparable to SimpleMKL. Kernel DRO uses RKHS to optimize under distributional uncertainty.
problem Optimizing under distributional uncertainty with limited knowledge.
method Kernel DRO using RKHS ambiguity sets and duality theory.
result Unified approach to robust and stochastic optimization.
Financial losses follow earthquake-like patterns, study finds.
problem Analyzing the timing between financial market losses.
method Fitting empirical interevent times with a Hawkes process.
result Financial market losses exhibit long-term memory similar to earthquakes.
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
A new framework learns differentiable structured losses from data.
problem Learning effective losses for complex structured prediction tasks.
method Contrastive learning to learn differentiable structured losses from output data.
result Achieves similar or better performance than kernel-based methods.
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.
Paper proposes a novel framework for structure learning using unstructured kernel-based M-regression.
problem Identifying underlying structures of true target functions from observed data.
method General and novel framework using unstructured M-regression in RKHS, inspired by gradient functions.
result Asymptotic results established for a wide range of loss functions, including mean, quantile, likelihood, and margin-based methods.
Optimizes differentially private kernel learning with random projection.
problem Privacy-preserving learning algorithms with optimal performance.
method Differentially private kernel ERM algorithm based on random projection in reproducing kernel Hilbert space.
result Achieves minimax-optimal excess risk rates for various loss functions.
Enhanced Hopfield model boosts memory retrieval capacity.
problem Memory retrieval in modern Hopfield models with limited capacity.
method Introduces a learnable feature map transforming energy function into kernel space, minimizing separation loss for uniform memory distribution.
result Significant reduction in metastable states, enhancing memory capacity and retrieval accuracy.
Gradient descent learns over-param neural nets better than NTK.
problem Learning over-parametrized neural networks with ReLU activations.
method Gradient descent from random initialization on a Gaussian input distribution.
result Gradient descent achieves population loss o(1/d), while NTK achieves Ω(1/d).