Related papers: Robust Numerical Methods for Nonlinear Regression
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data…
Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…
Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…
Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field…
This paper reports on application of bootstrap nonlinear regression method to a design of an experiment dataset with fewer experimental runs. Design with desired properties was augmented and verified using graphical techniques. The…
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…