Related papers: On the optimal shape parameter for kernel methods:…

Kolmogorov-Arnold Networks (KANs) approximate multivariate functions using learnable univariate edge functions, typically parameterized by B-spline bases. Although effective, spline-based implementations can be computationally expensive. A…

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…

Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…

We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable…

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…

We investigate statistical properties for a broad class of modern kernel-based regression (KBR) methods. These kernel methods were developed during the last decade and are inspired by convex risk minimization in infinite-dimensional Hilbert…

In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions…

Gravitational field modelling is an important tool for inferring past and present dynamic processes of the Earth. Functions on the sphere such as the gravitational potential are usually expanded in terms of either spherical harmonics or…

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…

A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our…

Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…

This paper deals with the optimal synthesis of aperture fields for (radiating) near-field communications in obstructed environments. A physically consistent model based on knife-edge diffraction is used to formulate the problem as a…

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…

We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…

The kernel-based regularization method has two core issues: kernel design and hyperparameter estimation. In this paper, we focus on the second issue and study the properties of several hyperparameter estimators including the empirical Bayes…