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.
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48 results for “kernel mean-p power error”
Neural network for water treatment anomaly detection with GA architecture optimization.
problem Detect anomalies in water treatment systems.
method Genetic algorithms for NN architecture optimization, NAB metric, F1-metric drawbacks analysis, techniques to improve AD quality.
result Improved anomaly detection quality through genetic algorithms and techniques.
New algorithms improve robust distributed estimation in impulsive noise.
problem Robust distributed estimation in impulsive noise environments.
method Diffusion maximum correntropy criterion algorithms.
result Outperforms existing robust diffusion algorithms.
New insights into CI tests reveal key factors for practical performance.
problem Understanding and improving CI tests in practical applications.
method Investigation of the Kernel-based Conditional Independence (KCI) test and analysis of its practical behavior.
result Errors in conditional mean embedding estimates and appropriate conditioning kernel selection are crucial for CI tests.
Estimates kernel eigenvalues for compositional dot-product kernels.
problem Improving estimates for kernel eigenvalues.
method Eigenvalue decay estimates of integral operators associated with dot-product kernels.
result Improved estimates for kernel volumes in reproducing kernel Hilbert spaces.
Proofs Fisher-Rao distance on Gaussian covariance manifold.
problem Proving Fisher-Rao distance on Gaussian covariance manifold.
method Basic Riemannian geometry.
result Proof of Fisher-Rao distance on covariance cone.
Improved error bounds for random Fourier features.
problem Scalability issues with kernel methods for large datasets.
method Improved uniform error bound and variance analysis of random Fourier features.
result The more widely used variant of random Fourier features is strictly higher-variance for the Gaussian kernel and has worse bounds.
Robust tests control type I error under data corruption.
problem Effective hypothesis testing under data corruption.
method General permutation tests using kernel MMD and HSIC metrics.
result Robust tests are minimax optimal and outperform private tests.
Paper proposes a new method for learning kernels that depend on both inputs and outputs.
problem Common kernels are limited in their ability to handle complex tasks.
method Developed a spectral kernel learning framework that uses non-stationary kernels and learns from data.
result Derived a data-dependent generalization error bound and suggested regularization terms.
New ensemble SVM model reduces prediction error without choosing best kernel.
problem Reducing prediction error in regression problems.
method Bagged-weighted support vector regression model with random machines.
result Regression Random Machines achieve lower generalization error.
Generalized Kernel Thinningstat.ML
Improves probability distribution compression with KT algorithm.
problem Efficiently compressing probability distributions.
method Kernel thinning (KT) algorithm with four improvements.
result KT yields tighter, dimension-free guarantees for any kernel.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
Gradient descent benefits from tangent kernel advantages under specific conditions.
problem Comparing gradient descent with tangent kernel methods in learning.
method Analysis of gradient descent and tangent kernel methods under different conditions.
result Gradient descent can achieve small error only if tangent kernel methods have a non-trivial advantage, but this advantage can be very small.
A new witness two-sample test improves data efficiency and power.
problem Nonparametric two-sample testing.
method Optimizes kernel and defines weights and basis points using training data.
result The new test is consistent, has well-controlled type-I error, and has comparable or higher power.
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
A new kernel test reduces noise in MMD by focusing on leading eigen-directions.
problem Noise in trailing directional components degrades power of standard kernel two-sample tests.
method Truncate MMD spectral decomposition, retaining only leading eigen-directions.
result Our method achieves superior power and robustness, especially in high-dimensional and unbalanced settings.
The paper explores how kernel eigenalignments affect generalization in KRR.
problem Achieving robust generalization in kernel methods.
method Direct connection between generalization and matrix eigenvectors/eigenvalues, focusing on finite-sample settings.
result Strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between eigenvalues.
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.
Two-sample tests using MMD control type I error and achieve optimal power.
problem Developing reliable nonparametric two-sample tests for small sample sizes.
method Maximum Mean Discrepancy (MMD) for constructing novel nonparametric tests, proving non-asymptotic error control and optimality.
result MMDAgg test controls type I error and achieves minimax rate over Sobolev balls, outperforming other tests.
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.
Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regimestat.ML
The study examines Kernel Ridge Regression error rates across noiseless and noisy conditions.
problem Characterizing Kernel Ridge Regression error rates in different noise levels.
method Unified analysis of Kernel Ridge Regression under various noise and regularization conditions.
result A crossover from noiseless to noisy error rates is observed as sample complexity increases.
Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize…
A new convolutional spectral kernel network learns hierarchical and local features.
problem Lack of deep learning in non-stationary spectral kernels.
method Introduces convolutional filters and deep architectures into non-stationary spectral kernels, derives generalization error bounds, and introduces regularizers.
result Validated the effectiveness of the convolutional spectral kernel network on real-world datasets.
Kernel Tests of Equivalencestat.ML
Kernel tests assess equivalence between distributions without assuming specific moments.
problem Traditional goodness-of-fit tests fail to detect meaningful distributional differences.
method Proposes kernel-based tests using kernel Stein discrepancy and Maximum Mean Discrepancy.
result Tests assess the absence of meaningful distributional differences under controlled error rates.
Proposes DR-ME test for interpretable distributional treatment effects.
problem Detects invisible differences in treatment effects on distributional outcomes.
method Semiparametrically efficient finite-location test using kernel witnesses and orthogonal features.
result DR-ME reveals causal-discrepancy coordinates and has noncentral chi-square local power.
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
problem Testing conditional independence
method Testing-by-betting on an adaptively optimized Kernel Conditional Independence statistic
result Significantly reduces Type I error inflation while preserving high power
The paper explores properties of curves and surfaces of constant width using Fourier series.
problem Investigating properties of curves and surfaces of constant width.
method Utilizing Fourier series to derive properties and proving theorems.
result The density of a certain packing of Reuleaux triangles exceeds the maximum density for circles.
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate over multinomial and bounded-support alternatives.
KRLS improves adaptive signal processing with kernel methods, reducing complexity.
problem High computational complexity in KRLS.
method Regularization and sparsification techniques to reduce complexity.
result Reduced computational complexity and memory consumption.
The paper provides tighter error bounds for GPR under bounded support noise.
problem Rigorous error quantification for safety-critical applications with bounded noise.
method Using concentration inequalities and low complexity assumptions in RKHS, the paper derives probabilistic and deterministic error bounds for GPR.
result The derived error bounds are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels.
Convolution and pooling improve kernel methods in image classification.
problem Understanding the interplay between approximation and generalization in convolutional architectures.
method Characterized RKHS of kernels with convolution, pooling, and downsampling, computed generalization error.
result Convolution and pooling operations trade off approximation with generalization power.
Kernel method tests if two sets of data are from the same distribution.
problem Two-sample hypothesis testing for high dimensional data with small samples.
method One-class set classification using Set Kernel and one-class SVM.
result The method achieves zero type-I and type-II error on all cancer gene expression data sets.
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample s…
Paper bounds the minimal rank for kernel ridge regression approximations.
problem Efficient memory and computation for kernel ridge regression.
method Lower bound on minimal rank for reliable prediction power.
result Nyström method's computational cost is almost linear in sample size.
New insights into how overfitting affects neural networks' performance.
problem Understanding the generalization of overfitted two-layer neural networks.
method Analyzing the NTK model with ReLU activation, focusing on min -norm solutions.
result Generalization error of overfitted NTK models approaches a small limiting value, even with infinite neurons and samples.
Automates kernel discovery for longitudinal data analysis.
problem Handling irregularly sampled, sparse longitudinal data with multilevel correlation.
method Combines deep neural networks and non-parametric kernel methods to discover complex multilevel correlation structure.
result Significantly outperforms state-of-the-art methods on benchmark data sets.
Sparse Gaussian processes with compact kernels for faster inference.
problem Efficient Gaussian process inference with high computational complexity.
method Parametric families of compactly-supported kernels for sparse matrix representations.
result Sub-quadratic inference complexity and improved performance on real-world tasks.
New framework reveals faster learning rate for deep learning models.
problem Analyzing the generalization error of deep learning models.
method Developed a new theoretical framework based on reproducing kernel Hilbert spaces.
result Derive a faster learning rate for deep learning algorithms.
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…
Paper develops a new kernel approximation framework.
problem High time and space complexity of kernel methods for large datasets.
method Perturbation-based kernel approximation framework using classical perturbation theory.
result Framework generalizes and improves upon existing methods.
A new method for anomaly detection adapts to local non-stationarity in low-data regimes.
problem Adapting conformal anomaly detection to handle distribution shifts in real-world data.
method Proposes a continuous inference relaxation using continuous weighted kernel density estimation to decouple local adaptation from tail resolution.
result Restores detection capabilities and statistical power in low-data regimes while maintaining valid error control.
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa…
The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. Th…
A hybrid scheme improves accuracy in simulating Brownian semistationary processes.
problem Simulating Brownian semistationary processes with high accuracy.
method Discretizing the stochastic integral representation using a hybrid scheme of power and step functions.
result The hybrid scheme leads to a substantial improvement in accuracy compared to the forward Riemann-sum scheme.
Study on expressive power of Euclidean kernels and efficient kernel learning.
problem Limiting the expressive power of kernel methods and improving kernel learning efficiency.
method Define Euclidean kernels, analyze their geometric and spectral properties, and develop efficient algorithms for kernel learning.
result Prove limitations on the expressive power of Euclidean kernels and derive efficient algorithms for kernel learning.
New TTP framework fuses control arms while controlling Type-I error.
problem Bias in borrowing control data from previous trials.
method Kernel two-sample testing via MMD and equivalence testing.
result Higher power than standard TTP methods while maintaining error control.
Efficiently approximates kernel mean embeddings using Nyström method.
problem Computational cost of kernel mean embeddings in large-scale settings.
method Nyström method for approximating a small random subset of the dataset.
result Upper bound on approximation error with sufficient subsample size conditions.
This paper improves active learning for Gaussian process regression to handle distributional uncertainty.
problem Active learning for Gaussian process regression does not guarantee accurate predictions for target distributions.
method Proposes two methods to reduce worst-case expected error for Gaussian process regression.
result Shows an upper bound of the worst-case expected squared error, suggesting finite data labels can achieve arbitrarily small error.