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 regression”
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.
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 …
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.
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 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.
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.
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 …
Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine (ELM) are popular techniques. However, the noise sensitivity is a major bottlene…
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…
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is that when a nonparame…
Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between …
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are u…
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence in various machine learning algorithms like generalized least squa…
Novel method for time-series prediction with tighter confidence intervals.
problem Improving prediction intervals for time-series data.
method Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI) using adaptive weights.
result KOWCPI achieves narrower confidence intervals with guaranteed coverage.
Improved learning theory for kernel distribution regression with two-stage sampling.
problem Distribution regression problem and two-stage sampling setting.
method Kernel methods, near-unbiased condition, new error bounds, convergence rates.
result Strictly improved convergence rates for three important classes of kernels.
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…
Aggregates predictions from multiple regression models using random projections and kernel methods.
problem Combining predictions from multiple regression models to improve accuracy.
method Random projection of high-dimensional feature space, followed by kernel-based consensual aggregation.
result The aggregation scheme performs similarly to using the original high-dimensional features, with high probability.
Paper introduces new regression methods for consistent estimation of biophysical parameters.
problem Estimating biophysical parameters while respecting auxiliary variables.
method Linear and nonlinear kernel-based regression models with consistency constraints.
result Models provide closed-form solutions and successfully estimate chlorophyll content.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
Kernel-based test detects differences between two conditional distributions efficiently.
problem Detecting differences between two conditional distributions efficiently.
method Kernel-based measure using nearest-neighbor graphs, consistent estimate with Gaussian limit.
result Asymptotic level control and universal consistency for detecting differences.
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…
We present a novel algorithm for non-linear instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that two-stage procedures for non-linear IV regression can be reformulated as a convex-concave saddle-…
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess t…
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.
The objective of this study is to investigate the efficient determination of and for Support Vector Regression with RBF or mahalanobis kernel based on numerical and statistician considerations, which indicates the connection between and kernels and demonstrates that the deviation of geometric distance of ne…
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
Highly Adaptive Ridgestat.ML
HAR regression improves performance on small datasets.
problem Small datasets with complex functions.
method Data-adaptive kernel ridge regression using tensor-product spline basis.
result Achieves convergence rate for right-continuous functions.
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.
Boosting combines weak (biased) learners to obtain effective learning algorithms for classification and prediction. In this paper, we show a connection between boosting and kernel-based methods, highlighting both theoretical and practical applications. In the context of boosting, we start with a weak linear le…
Method approximates high-dimensional feature vectors for supervised learning.
problem Reducing storage and computational complexity in high-dimensional data.
method Approximates feature vectors using a kernel-based approach to reduce data size.
result Significant improvements in classification and regression tasks.
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basi…
TNP-KR improves scalability of NPs with Transformer blocks and attention mechanisms.
problem Scalability bottleneck in NPs and GPs, especially for large datasets.
method Introduces TNP-KR with KRBlock, kernel-based attention, and two attention mechanisms.
result TNP-KR with DKA outperforms Performer and achieves state-of-the-art results.
We propose an efficient nonparametric strategy for learning a message operator in expectation propagation (EP), which takes as input the set of incoming messages to a factor node, and produces an outgoing message as output. This learned operator replaces the multivariate integral required in classical EP, which may not…
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…
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 bounds for kernel regression under non-Gaussian noise.
problem Uncertainty quantification for function estimates from noisy observations.
method Novel non-asymptotic probabilistic uniform error bounds for kernel-based regression.
result Proposed bounds apply to a broad class of non-Gaussian noise distributions.
New tests compare regression functions using machine learning, overcoming dimensionality issues.
problem Comparing regression functions in high-dimensional settings.
method Generalized kernel-based conditional mean dependence, machine learning methods for flexible estimation.
result Established asymptotic properties of tests under fixed and high-dimensional regimes.
New method for causal inference with complex treatment compositions.
problem Estimating causal effects with compositional treatments.
method Kernel-based covariate functional balancing approach.
result Achieves -consistency without requiring consistent estimation of weights.
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensio…
GaussDetect-LiNGAM eliminates Gaussianity tests for causal discovery.
problem Causal direction identification without Gaussianity assumptions.
method Leverages the equivalence between noise Gaussianity and residual independence in reverse regression.
result Gaussianity tests replaced with robust kernel-based independence tests.
Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local contr…
The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switch…
Combines Gaussian process and Geometric Harmonics for better uncertainty estimation.
problem Uncertainty estimation in kernel-based methods.
method Combines Gaussian process and Geometric Harmonics.
result Alternative interpretations of uncertainty and accelerated Bayesian Optimization.
There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for …