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 n∼logp samples. Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.
problem Selecting an appropriate kernel for Kernelized Diffusion Maps.
method Two complementary approaches: variational outer loop and unsupervised cross-validation.
result Both methods improve the quality and stability of the recovered eigenfunctions.
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 method for faster bandwidth selection in Gaussian kernel ridge regression.
problem Efficiently selecting the bandwidth in Gaussian kernel ridge regression.
method Formulated an approximate Jacobian expression for bandwidth selection, proposing a closed-form heuristic.
result Our method is as accurate as cross-validation and marginal likelihood maximization but up to six orders of magnitude faster.
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.
A new method optimizes MMD test power by dynamically selecting kernels, overcoming traditional trade-offs.
problem Fixed kernels fail to distinguish certain distributions, leading to overfitting and variance collapse.
method Complexity-Penalized MMD (CP-MMD) criterion, derived from concentration inequality, optimizes kernel selection.
result CP-MMD maximizes true test power while ensuring unconditional Type-I validity, matching or exceeding state-of-the-art performance.
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
To cluster data that are not linearly separable in the original feature space, k-means clustering was extended to the kernel version. However, the performance of kernel k-means clustering largely depends on the choice of kernel function. To mitigate this problem, multiple kernel learning has been introduced into th…
New active learning method for kernel selection improves efficiency and accuracy.
problem Real-world applications where acquiring true labels is costly or time-consuming.
method Active Multiple Kernel Learning (AMKL) with adaptive kernel selection (AMKL-AKS).
result AMKL-AKS achieves optimal sublinear regret and better performance with fewer labeled data.
New method for efficient personalized learning in mobile health.
problem Efficient and personalized learning in mobile health.
method Proposes a novel generative process on kernel composition for online Gaussian Process regression.
result Trajectories of kernel evolutions can be transferred between users to improve learning and kernels are meaningful for mHealth prediction.
Proposes a method to select variables for kernel two-sample tests.
problem Determining whether two samples have the same distribution using informative variables.
method A framework based on kernel maximum mean discrepancy (MMD) for selecting a subset of variables.
result The sample size requirements for the three kernels depend on the number of selected variables, not the data dimension.
This paper uses MIO to select features for kernel SVM classification.
problem Feature selection for kernel SVM classification.
method Mixed-integer optimization (MIO) for feature subset selection.
result The MIO approach can often outperform linear-SVM-based methods in prediction performance.
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…
We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernel…
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.
Paper proposes a new landmark selection method for kernel ridge regression.
problem Efficient landmark selection for scalable kernel methods.
method Two-step approach: first computes importance scores, then clusters them into landmarks.
result Proposed method provides better accuracy and efficiency trade-offs.
Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.
problem Manual selection of kernels in Gaussian processes is complex and computationally expensive.
method Proposes a novel method using symbolic representation and Bayesian optimization to search through a structured kernel space.
result Empirically shows a computationally more efficient way of searching through a discrete kernel space.
A method selects key genes from tumor transcriptomics data using kernel methods and improves classification performance.
problem Feature selection for tumor classification using gene expression data.
method Multiple Kernel Learning with latent regularization and non-linear dimensionality reduction.
result Improved tumor classification performance on unseen test samples.
Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally efficient?". First, we show that a Biweight kernel is optimal in the sense of minim…
Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches. However, selecting kernels is non-trivial in practice. Although kernel selection fo…
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this pa…
Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD class…
BOOST automates kernel and acquisition function selection in Bayesian optimization.
problem Inappropriate kernel and acquisition function combinations lead to poor performance in Bayesian optimization.
method BOOST uses offline evaluation to predict and select the best kernel-acquisition function pair.
result BOOST consistently improves over fixed-hyperparameter BO and is competitive with state-of-the-art adaptive methods.
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel…
Kernel ridge regression for causal inference with missing data.
problem Estimating treatment effects with missing data in selected samples.
method Kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects.
result Uniform consistency and finite sample rates for continuous treatment, root-n consistency for discrete treatment.
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms cannot attain these properties at the same time. In this article, a three-step va…
Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel function is of great importance, especially for the finite sample settings commonly e…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostl…
Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the significant modalities of the data. In such applications, each base kernel repre…
PEAKS selects key training examples incrementally based on prediction error and kernel similarity.
problem Dynamic data selection in deep learning models.
method Prediction Error Anchored by Kernel Similarity (PEAKS) for incremental data selection.
result PEAKS outperforms existing selection strategies and yields better performance returns as training data size grows.
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the tra…
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
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…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random varia…
New method selects optimal bandwidth for price return density estimation, impacting efficient market hypothesis evaluation.
problem Estimating the complexity of price return distributions using kernel density estimation.
method Proposes a new complexity measure to select optimal bandwidth, avoiding overfitting and underfitting.
result Optimal bandwidth selection leads to clearer evaluation of the efficient market hypothesis.
Paper learns optimal kernels for Gaussian process regression in aerodynamics.
problem Approximating complex functions from limited data in aerodynamics.
method Two algorithms: Kernel Flow and Spectral Kernel Ridge Regression.
result Explicit construction of optimal kernels based on target function features.
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…
The paper introduces a new method for feature selection without explicit sparsification.
problem Feature selection with implicit sparsity-inducing mechanisms.
method Optimization over a family of kernels with gradient descent.
result The method achieves exact sparsity without explicit penalization techniques.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
problem Efficiently approximating positive definite kernels for large datasets.
method Refined sampling and subspace selection in Nyström approximation.
result Novel theoretical guarantees for non-i.i.d. landmark points in kernel quadrature.
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
Counterexamples show HSIC feature selection misses critical features.
problem Feature selection using HSIC misses important features.
method Feature selection via HSIC maximization.
result HSIC feature selection can miss critical features.
New method for sparse kernel selection improves prediction accuracy.
problem Sparse Multiple Kernel Learning for binary classification.
method Alternating best response algorithm with semidefinite relaxations.
result Method outperforms state-of-the-art MKL approaches in prediction accuracy.
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when direc…