26 papers · ranked by Valyu relevance
Kaan Gökcesu, Hakan Gökcesu
—We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex nonlinear regression model exists for the traditional least squares problem, which can…
Timothy E. O’Brien, Jack W. Silcox
Use of nonlinear statistical methods and models are ubiquitous in scientific research. However, these methods may not be fully understood, and as demonstrated here, commonly-reported parameter p-values and confidence intervals may be inaccurate. The gentle introduction to nonlinear regression modelling and…
Authors not listed
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 statistical modeling and computation. Least squares with the Gauss-Newton method is the…
Hamdy F. F. Mahmoud
Three types of regression models researchers need to be familiar with and know the requirements of each: parametric, semiparametric and nonparametric regression models. The type of modeling used is based on how much information are available about the form of the relationship between response variable and explanatory…
Jayri Bagchi, Tapas Si
Regression analysis is an important machine learning task used for predictive analytic in business, sports analysis, etc. In regression analysis, optimization algorithms play a significant role in search the coefficients in the regression model. In this paper, nonlinear regression analysis using a recently developed…
Noah A. Schuster, Judith J. M. Rijnhart, Jos W. R. Twisk, Martijn W. Heymans
'Martijn W. Heymans'] Objective Traditional methods to deal with non-linearity in regression analysis often result in loss of information or compromised interpretability of the results. A recommended but underutilized method for modeling non-linear associations in regression models is spline functions. We explain…
William W. Hsieh
When applying machine learning/statistical methods to the environmental sciences, nonlinear regression (NLR) models often perform only slightly better and occasionally worse than linear regression (LR). The proposed reason for this conundrum is that NLR models can give predictions much worse than LR when given input…
Menoua Keshishian, Hassan Akbari, Bahar Khalighinejad, Jose Herrero + 2 more
Sensory processing by neural circuits includes numerous nonlinear transformations that are critical to perception. Our understanding of these nonlinear mechanisms, however, is hindered by the lack of a comprehensive and interpretable computational framework that can model and explain nonlinear signal transformations.…
Aaditya Prasad Gupta
Biological systems, at all scales of organization from nucleic acids to ecosystems, are inherently complex and variable. Therefore mathematical models have become an essential tool in systems biology, linking the behavior of a system to the interaction between its components. Parameters in empirical mathematical models…
Peng Zheng, Ryan Barber, Reed Sorensen, Christopher Murray + 1 more
Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and…
William Casey, Leigh Metcalf, Shirshendu Chatterjee, Heeralal Janwa + 3 more
Many real-world problems feature nonlinear dynamic processes. Classical mathematical models may be adequate to describe a single dynamic process in isolation, but can be easily undermined by two natural and simple kinds of phenomenological variations: the emergence (or activation) of an additional dynamic process, and…
Nicholas C Chesnaye, Merel van Diepen, Friedo Dekker, Carmine Zoccali + 2 more
'Carmine Zoccali' 'Kitty J Jager' 'Vianda S Stel'] Title: ABSTRACT True linear relationships are rare in clinical data. Despite this, linearity is often assumed during analyses, leading to potentially biased estimates and inaccurate conclusions. In this introductory paper, we aim to first describe-in a non-mathematical…
Noah A. Schuster, Judith J. M. Rijnhart, Lisa C. Bosman, Jos W. R. Twisk + 2 more
'Jos W. R. Twisk' 'Thomas Klausch' 'Martijn W. Heymans'] Background Confounding is a common issue in epidemiological research. Commonly used confounder-adjustment methods include multivariable regression analysis and propensity score methods. Although it is common practice to assess the linearity assumption for the…
Alina Malyutina, Jing Tang, Alberto Pessia
Analysis of dose-response data is an important step in many scientific disciplines, including but not limited to pharmacology, toxicology, and epidemiology. The R package drda is designed to facilitate the analysis of dose-response data by implementing efficient and accurate functions with a familiar interface. With…
Authors not listed
Plastic mechanical recycling is the conventional technological step towards circularity. In such aspects, complex mixtures of polyolefin blends are often fed into mechanical recycling systems, resulting in moulded products with uncertain quality. To add to the difficulty of heterogeneous feedstocks, the testing of…
Ikechukwu I. Udema
A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v…
Kevin Robben, Christopher Cheatum
We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo lineshape models and introduce a novel least-squares fitting metric, termed the Scale Invariant Gradient Norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Trung C. Phan, Adrian Pranata, Joshua Farragher, Adam Bryant + 3 more
Machine learning (ML) algorithms are crucial within the realm of healthcare applications. However, a comprehensive assessment of the effectiveness of regression algorithms in predicting alterations in lifting movement patterns has not been conducted. This research represents a pilot investigation using regression-based…
Authors not listed
Learning aqueous solubility remains a key challenge in drug development for improving oral bioavailability. Traditional data-driven solubility estimations using standard supervised models, however, can often suppress the information embedded in a molecule’s chemical properties and the intricate connectivity of its…
Muhammad Hanzla, Abdul Rehman Shinwari
Machine Learning (ML) can be defined as a class of Artificial Intelligence for automated data analysis, which is capable of detecting patterns in data. The extracted patterns can be used to predict un-known data or to assist in decision-making processes under uncertainty. Recent advances in experimental and…
Authors not listed
Nonlinear monotonically increasing bounded functions help to visualize and analyze data on various scales. However, many monotonic functions such as logarithm or power laws have either function values or derivatives that become unbounded at some regions of the $x-$ axis. On the other hand, sigmoid or hyperbolic…
Wang, Jingyuan, Ji, Jiahao
This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition) at the School of Computer Science and Engineering, Beihang University. It aims to provide students – who are…
Erfan Nozari, Jennifer Stiso, Lorenzo Caciagli, Eli J. Cornblath + 5 more
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. One may therefore expect the collective dynamics of massive networks…
Akhila Henry, Nithin Nagaraj
This study presents novel Augmented Regression Models using Neurochaos Learning (NL), where Tracemean features derived from the Neurochaos Learning framework are integrated with traditional regression algorithms —- Linear Regression, Ridge Regression, Lasso Regression, and Support Vector Regression (SVR). Our approach…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…