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

The causal inference literature frequently focuses on estimating the mean of the potential outcome, whereas quantiles of the potential outcome may carry important additional information. We propose a unified approach, based on the inverse…

Using the Laplace derivative a Perron type integral, the Laplace integral, is defined. Moreover, it is shown that this integral includes Perron integral and to show that the inclusion is proper, an example of a function is constructed,…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…

Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this paper is to propose the definition of a score…

Performativity of predictions refers to the phenomenon where prediction-informed decisions influence the very targets they aim to predict -- a dynamic commonly observed in policy-making, social sciences, and economics. In this paper, we…

We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This…

This note contributes to a circle of ideas that we have been developing recently in which we view certain abstract operator algebras $H^{\infty}(E)$, which we call Hardy algebras, and which are noncommutative generalizations of classical…

A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…

In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…

Dyson's integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index…

We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…

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…

An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel $|K_{(i\tau+\alpha)/2}(x)|^2, \alpha \ge 0,\ x…

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…