Related papers: A note on averaging prediction accuracy, Green's f…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…

The safe integration of machine learning modules in decision-making processes hinges on their ability to quantify uncertainty. A popular technique to achieve this goal is conformal prediction (CP), which transforms an arbitrary base…

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…

Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…

Consider a non-linear operator equation $x - K(x) = f$, where $f$ is a given function and $K$ is a Urysohn integral operator with Green's function type kernel defined on $L^\infty [0, 1]$. We apply approximation methods based on…

This letter describes a direct method for computing the spatially averaged outage probability of a network with interferers located according to a point process and signals subject to fading. Unlike most common approaches, it does not…

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation…

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential…

We consider the eigenvalue problem $K x = \lambda x$. Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator $K$ with Green's kernels. By employing orthogonal…

The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…

Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…

This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…

A key component of automated algorithm selection and configuration, which in most cases are performed using supervised machine learning (ML) methods is a good-performing predictive model. The predictive model uses the feature representation…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…