Related papers: Optimal kernel regression bounds under energy-boun…

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…

Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…

We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the…

If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…

Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…

This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

In this work, we revisit the problem of active sequential prediction-powered mean estimation, where at each round one must decide the query probability of the ground-truth label upon observing the covariates of a sample. Furthermore, if the…

Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…