Related papers: Laplace's formula: an approach by nonstandard anal…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
We show that, if PA has no non-standard models, then P=/=NP. We then give an elementary proof that PA has no non-standard models.
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
Fitting cross-classified multilevel models with binary response is challenging. In this setting a promising method is Bayesian inference through Integrated Nested Laplace Approximations (INLA), which performs well in several latent variable…
This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
The S-measure construction from nonstandard analysis is used to prove an extension of a result on the intersection of sets in a finitely-additive measure space. This is then used to give a density-limit version of a representation theorem…
Understanding the dynamics of the land-atmosphere exchange of CO$_2$ is key to advance our predictive capacities of the coupled climate-carbon feedback system. In essence, the net vegetation flux is the difference of the uptake of CO$_2$…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
An important feature of successful supervised machine learning applications is to be able to explain the predictions given by the regression or classification model being used. However, most state-of-the-art models that have good predictive…
We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.
To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct such examples. It is based on the regularity theory for…
An explanation to Lord's paradox using ordinary least square regression models is given. It is not a paradox at all, if the regression parameters are interpreted as predictive or as causal with stricter conditions and be aware of laws of…
Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and…
We review standard subtraction, as a method to compute cross sections at NNLO accuracy.
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…