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

In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the $(\kappa, a)$-generalized Fourier transform for $\kappa =0$. In the case of dihedral groups, this method is also applied to the Dunkl…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

In recent years, machine learning researchers have focused on methods to construct flexible and interpretable prediction models. However, an interpretability evaluation, a relationship between generalization performance and an…

While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where datasets pertaining…

We adapt Gaussian processes for estimating the average dose-response function in observational settings, introducing a powerful complement to treatment effect estimation for understanding heterogeneous effects. We incorporate samples from a…

Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…

We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the…

We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be…

Research in both machine learning and psychology suggests that salient examples can help humans to interpret learning models. To this end, we take a novel look at black box interpretation of test predictions in terms of training examples.…

Artificial intelligence, particularly through recent advancements in deep learning, has achieved exceptional performances in many tasks in fields such as natural language processing and computer vision. In addition to desirable evaluation…

Prediction intervals are a machine- and human-interpretable way to represent predictive uncertainty in a regression analysis. In this paper, we present a method for generating prediction intervals along with point estimates from an ensemble…

In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while…

Let $(X_t)_{t\geq0}$ be the $n$-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space $\D^n$ having the Laplace-Beltrami operator as its generator. The aim of the paper is to derive the formulas for the…

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…

In the field of machine learning, regression problems are pivotal due to their ability to predict continuous outcomes. Traditional error metrics like mean squared error, mean absolute error, and coefficient of determination measure model…

We introduce a hull operator on Poisson point processes, the easiest example being the convex hull of the support of a point process in Euclidean space. Assuming that the intensity measure of the process is known on the set generated by the…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

Information compression plays a central role in diverse fields of modern science and technology, from communication theory to machine learning. In condensed-matter physics, the intermediate representation (IR) basis has recently been…