This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Expe…
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48 results for “Kernel-based”
Paper shows robustness of kernel-based pairwise learning without strict assumptions.
problem Statistical robustness of kernel-based pairwise learning under minimal conditions.
method No assumptions on input and output spaces; derives influence function and robustness.
result Qualitative robustness of kernel-based estimator established.
New algorithm improves dynamic mode decomposition for high-dimensional data.
problem Reduced modeling in high-dimensional spaces.
method Low rank constraint optimization and kernel-based computation.
result Gain in approximation accuracy and computational efficiency.
Kernel-based function approximation improves reinforcement learning performance.
problem Average reward reinforcement learning in infinite horizon settings.
method Optimistic algorithm based on kernel ridge regression.
result No-regret performance guarantees and confidence intervals for kernel-based predictions.
Kernel-based online learning has often shown state-of-the-art performance for many online learning tasks. It, however, suffers from a major shortcoming, that is, the unbounded number of support vectors, making it non-scalable and unsuitable for applications with large-scale datasets. In this work, we study the problem …
Study provides guarantees for kernel clustering under non-parametric mixtures.
problem Statistical guarantees for kernel-based clustering without strong assumptions.
method Non-parametric mixture models, kernel-based clustering, consistency guarantees.
result Necessary and sufficient separability conditions for consistent clustering recovery.
Kernel-based algorithms improve integral estimation with near-geometric speed.
problem Estimating integrals with target measures that are nearly atomic.
method Weighted kernel herding and sequential Bayesian quadrature.
result Near-geometric rate of convergence for nearly atomic target measures.
Kernel-based L2-boosting with structure constraints improves regression efficiency.
problem Developing efficient kernel methods for regression.
method Kernel-based re-scaled boosting with truncation (KReBooT).
result KReBooT achieves near overfitting resistance and sparse estimates.
Novel confidence intervals improve convergence rates for sparse kernel-based models.
problem High computational cost in kernel-based learning models.
method Novel confidence intervals for Nyström method and sparse variational Gaussian process approximation.
result Improved performance bounds in regression and optimization problems.
Adaptive rule improves kernel-based gradient descent performance.
problem Improving convergence speed of kernel-based gradient descent algorithms.
method Empirical effective dimension for stopping rule, learning theory analysis, integral operator approach.
result Optimal learning rates and iteration bounds for KGD with adaptive stopping rule.
Toward a better trade-off between performance and fairness with kernel-based distribution matchingcs.LG
Paper introduces MinDiff framework for balancing classifier performance and fairness.
problem Balancing classifier performance and fairness in machine learning models.
method MinDiff framework with kernel-based statistical dependency tests.
result Demonstrates real-world improvements in classifier performance and fairness.
ConvNets can be translated into CKNs that perform similarly.
problem The distinction between ConvNets and kernel-based methods.
method Translation of ConvNets into CKNs using a new gradient algorithm.
result CKNs perform as well as ConvNets, supporting the translation.
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.
A new kernel-based CI test improves on existing methods.
problem Testing conditional independence (CI) in a broad range of dependencies.
method Regression-model-agnostic kernel-based CI test using reproducing kernel Hilbert spaces.
result GKCM outperforms state-of-the-art CI tests in simulations.
Taming Nonconvexity in Kernel Feature Selection -- Favorable Properties of the Laplace Kernelmath.ST
Laplace kernel feature selection offers statistical guarantees for nonparametric models with few samples.
problem Statistical guarantees for kernel-based feature selection in nonconvex optimization problems.
method Sharp characterization of the gradient of the objective function for Laplace kernel feature selection.
result Model-selection consistency for Laplace kernel-based feature selection in nonparametric settings with samples.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are effective at computing the expected value of a point at a future time given the …
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated with desired accuracy. Nevertheless, inherent to the nonparametric nature of kernel…
FastKCI speeds up KCI tests for causal inference on large datasets.
problem Cubic computational complexity of kernel-based conditional independence tests.
method Mixture-of-experts approach with parallel Gaussian process inference.
result Substantial computational speedups with maintained statistical power.
Paper proposes an efficient causal discovery method with linear computational complexity.
problem Identifying causal relationships efficiently in large datasets.
method Approximate kernel-based generalized score function with low-rank technique and sampling algorithms.
result Significantly reduces computational costs while maintaining comparable accuracy.
New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.
problem Inaccurate error bounds for kernel-based system identification with unknown hyperparameters.
method Construct a high-probability set for true hyperparameters from marginal likelihood, then find worst-case posterior covariance.
result Proposed bounds contain true model with high probability and verified in simulations.
Learning rates for the risk of kernel based quantile regression estimators in additive modelsstat.ML
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel …
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robust…
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.
Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the variance of the estimates and thus makes kernel-based methods particularly attract…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high computational complexity. Thus, the objective of this letter is to propose an fa…
This paper improves kernel-based regression using transfer learning.
problem Improving generalization performance in kernel-based regression.
method Two-step kernel-based estimator for known transferable sources and novel aggregation algorithm for unknown sources.
result Established statistical properties and validated effectiveness of proposed methods.
A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testingmath.ST
High-dimensional U-statistics show surprising phase transitions, impacting kernel-based tests.
problem Understanding phase transitions in high-dimensional U-statistics.
method Proved a convergence theorem for U-statistics of degree two in high dimensions.
result High-dimensional U-statistics can have non-Gaussian limits with larger variance and asymmetry.
Improved robustness in kernel-based regression via novel loss function and IRLS.
problem Noise sensitivity in kernel-based regression methods.
method Proposed -loss function and iteratively reweighted least squares (IRLS) optimization.
result Improved noise robustness in kernel-based regression methods.
Kernel-based tests for shape constraints in finance.
problem Enforcing shape relations on latent functions in financial econometrics.
method Kernel-based nonparametric framework for mean-variance optimization.
result Established statistical properties and a joint Wald-type statistic for testing shape constraints.
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the estimator using a few variables by l1-type penalized estimation. We see that the…
In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential …
Paper proposes adaptive parameter selection for KGD algorithms.
problem Improving parameter selection for kernel-based gradient descent.
method Integrates bias-variance analysis with splitting method, introduces empirical effective dimension.
result Adaptive parameter selection strategy achieves optimal generalization error bound.
Survey on graph kernels for graph classification tasks.
problem Graph classification tasks on graphs.
method Categorization and experimental evaluation of graph kernels.
result Simple baselines become competitive after Gaussian RBF kernel transformation on some datasets.
The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.
problem Fault detection in planetary gearboxes using vibration signals.
method Ensemble of three convolution kernel-based methods (ROCKET, 1D CNN with ResNet, FCN).
result Outperforms other approaches with over 98.8% accuracy.
New method identifies rare genetic markers for Alzheimer's disease using MRI and genomics.
problem Identifying rare genetic markers for Alzheimer's disease.
method Combining MRI data with genome sequencing, using CNNs for brain traits, and kernel-based tests for rare variants.
result CNNs provide precise brain traits and novel kernels identify rare genetic markers.
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample and independence tests from the machine learning community. A fixed-point transf…
Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrizationq-fin.CP
We propose kernel-based collocation methods for numerical solutions to Heath-Jarrow-Morton models with Musiela parametrization. The methods can be seen as the Euler-Maruyama approximation of some finite dimensional stochastic differential equations, and allow us to compute the derivative prices by the usual Monte Carlo…
New tools evaluate and optimize conditional sequence models in bioinformatics.
problem Evaluating and optimizing conditional sequence models in bioinformatics.
method Kernel-based discrepancy measure (ACMMD) to estimate model fit and tune hyperparameters.
result Rejects the hypothesis that ProteinMPNN fits its data for various protein families and optimizes model temperature.
We propose a simple kernel based nearest neighbor approach for handwritten digit classification. The "distance" here is actually a kernel defining the similarity between two images. We carefully study the effects of different number of neighbors and weight schemes and report the results. With only a few nearest neighbo…
This thesis improves kernel-based distances for statistical inference and integration.
problem Efficiently measuring distances between probability distributions for robust and smooth modeling.
method Kernel-based distances, focusing on maximum mean discrepancy (MMD) and novel kernel quantile discrepancies.
result Improved MMD estimators for simulation-based inference and conditional expectations.
Estimates system parameters from a single observation using kernel-based score.
problem Estimating parameters of a dynamical system from a high-dimensional signal.
method Kernel-based score to compare temporal dependencies between signal and model.
result Accuracy and efficiency demonstrated on chaotic systems.
Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.
problem Exploration-exploitation dilemma in finite-horizon reinforcement learning with metric state-action spaces.
method Kernel-UCBVI, leveraging smoothness and kernel estimators of rewards and transitions.
result First regret bound for kernel-based RL using smoothing kernels, .
Unified kernel-based methods improve nonlinear causal discovery.
problem Identifying nonlinear causal relationships between time series variables.
method Unified Kernel Principal Component Regression (KPCR) and Gaussian Process score-based model with Smooth Information Criterion.
result Improved performance in time series nonlinear causal discovery.
Paper proposes OKGAN to improve GAN training, addressing mode collapse and cycling.
problem Challenges in GAN training, including mode collapse and cycling.
method Kernel-based non-parametric discriminator for online training.
result OKGAN mitigates training issues and performs better than other GAN formulations.
Paper reproduces a kernel-based scan B-statistic for online change-point detection.
problem Continuous detection of distribution changes in online data streams.
method Efficient kernel-based scan B-statistic for online change-point detection.
result Scan B-statistic outperforms parametric methods in challenging scenarios.