Related papers: Nonparametric regression using needlet kernels for…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

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…

Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…

Time-series classification is essential across diverse domains, including medical diagnosis, industrial monitoring, financial forecasting, and human activity recognition. The Rocket algorithm has emerged as a simple yet powerful method,…

We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…

The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of…

Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…

Recent studies have reported $\textit{saturation effects}$ and $\textit{multiple descent behavior}$ in large dimensional kernel ridge regression (KRR). However, these findings are predominantly derived under restrictive settings, such as…

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

This paper proposes a ridgeless kernel method for solving infinite-horizon, deterministic, continuous-time models in economic dynamics, formulated as systems of differential-algebraic equations with asymptotic boundary conditions (e.g.,…