arXiv research

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

New method improves RL in continuous spaces with kernel smoothing.

Generative models use kernel smoothing for conditioning on small example sets.

New insights into simple kernel smoothing reveal surprising asymptotics.

SATL adapts to varying smoothness in hypothesis transfer learning.

Characterizes neural kernel and NNGP for various activations.

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-Gradient Drifting improves generative modeling for non-Euclidean data.

Kernel interpolation is inconsistent for norms with smoothness above a constant.

Smooth bundles with rough data maintain Hodge kernel isomorphism.

Enhances random forests by smoothing predictions for better performance.

Study shows infinite kernels in topological monodromy for curve families.

Improves probability distribution compression with KT algorithm.

The paper studies local heat kernel properties on smooth manifolds.

Paper proves KRR saturation effect for smooth functions.

New method improves optimization algorithms without Lipschitz smoothness.

The paper studies kernel smoothing and mean shift for directional data, deriving convergence rates and mode estimation.

New kernel improves MMDs with theoretical guarantees for gradient flows.

Extends Tanimoto kernel to real-valued functions.

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 …

The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.

Robust learning method combines kernel smoothing and robust optimization.

The paper studies heat kernels on modified manifolds and bounds their properties.

Improved kernel ridge regression for large datasets using weighted random binning.

Study shows quantum behavior near infinity in metric asymptotics.

Conditional COT-GAN predicts sequences using past data and kernel smoothing.

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$\sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high d…

Kernel-smoothed scores improve diffusion models by reducing memorization.

Paper introduces a new regularization method for kernel gradient descent learning.

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian …

Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built into their architectures or learned from previous experience. The learned weight…

New STKR estimators use unlabeled data for smoother function learning.

Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative. To fill in this void, we study here the asymptotic properties of goodness-of-fi…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, p…

New algorithm optimizes Hölder smooth functions in RKHS with tighter regret bounds.

Paper provides GOT convergence guarantees for sub-gamma distributions and dependent samples.

New method interpolates training data and is consistent for various data distributions.

We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature similarity or temporal information present in data sets, via non-parametric kernel sm…

The paper analyzes kernel classifiers' performance in Sobolev spaces and proves their optimality.

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific …

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with b…

fastkqr speeds up kernel quantile regression by up to 10x.

We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevr…

Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density.…

Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.

Adaptive kernel density estimation improves accuracy in high dimensions.

Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.

A new method warps inputs to learn nonstationary kernels efficiently.