Related papers: Interval straight line fitting
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
Numerical methods based on interval arithmetic are efficient means to reliably solve nonlinear systems of equations. Algorithm bc3revise is an interval method that tightens variables' domains by enforcing a property called box consistency.…
A fundamental challenge in deep learning is that the optimal step sizes for update steps of stochastic gradient descent are unknown. In traditional optimization, line searches are used to determine good step sizes, however, in deep…
Target trial emulation has improved comparative effectiveness research by making the causal question, assumptions, and analysis plan explicit. However, target trial protocols are usually developed iteratively. After examining the data,…
Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem,…
The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…
This paper develops a conformal method to compute prediction intervals for non-parametric regression that can automatically adapt to skewed data. Leveraging black-box machine learning algorithms to estimate the conditional distribution of…
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…