Related papers: Optimal Confidence Band for Kernel Gradient Flow E…

In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…

An interesting observation in artificial neural networks is their favorable generalization error despite typically being extremely overparameterized. It is well known that the classical statistical learning methods often result in vacuous…

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…

In this paper we establish asymptotic simultaneous confidence bands for the transformation kernel estimator of copulas introduced in Omelka et al.(2009). To this aim, we prove a uniform in bandwidth law of the iterated logarithm for the…

In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study…

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…

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

We study the worst case error of kernel density estimates via subset approximation. A kernel density estimate of a distribution is the convolution of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset (i.e. a point…

We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

Sign Gradient Descent (SignGD) is a simple yet robust optimization method, widely used in machine learning for its resilience to gradient noise and compatibility with low-precision computations. While its empirical performance is well…

In this paper, we consider contextual stochastic optimization using Nadaraya-Watson kernel regression, which is one of the most common approaches in nonparametric regression. Recent studies have explored the asymptotic convergence behavior…

To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating…