Related papers: Interpolation and Learning with Scale Dependent Ke…
We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…
We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional…
The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our…
We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require…
A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, it is commonly assumed…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…
A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the…
In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…
We study the average $\mbox{CV}_{loo}$ stability of kernel ridge-less regression and derive corresponding risk bounds. We show that the interpolating solution with minimum norm minimizes a bound on $\mbox{CV}_{loo}$ stability, which in turn…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
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…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…
This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…
We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error…
We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis…