Related papers: Kernel Ridge Riesz Representers: Generalization, M…
We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…
The proliferation of data has sparked significant interest in leveraging findings from one study to estimate treatment effects in a different target population without direct outcome observations. However, the transfer learning process is…
Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little…
In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…
This study clarifies the relationship between Riesz regression [Chernozhukov et al., 2021] and density ratio estimation (DRE) in causal inference problems, such as average treatment effect estimation. We first show that the Riesz…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy,…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference…
Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise…