Maximum likelihood estimation of probabilistic choice methods
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Transformation and weighting in regression
Transformation and weighting in regression
Sensitivity analysis in linear regression
Sensitivity analysis in linear regression
The PORT Mathematical Subroutine Library
ACM Transactions on Mathematical Software (TOMS)
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
ACM Transactions on Mathematical Software (TOMS)
Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach
ACM Transactions on Mathematical Software (TOMS)
Using Domain Knowledge on Population Dynamics Modeling for Equation Discovery
EMCL '01 Proceedings of the 12th European Conference on Machine Learning
Computational Optimization and Applications
Reducing overfitting in process model induction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Extracting constraints for process modeling
Proceedings of the 4th international conference on Knowledge capture
Machine Learning
Integrating Domain Knowledge in Equation Discovery
Computational Discovery of Scientific Knowledge
Mathematics and Computers in Simulation
Inducing hierarchical process models in dynamic domains
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Constructing explanatory process models from biological data and knowledge
Artificial Intelligence in Medicine
ILP'07 Proceedings of the 17th international conference on Inductive logic programming
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We present FORTRAN 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least-squares, maximum likelihood, maximum quasi-likelihood, generalized nonlinear least-squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (“nonlinear GLIM”), and probabilistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least-squares, employs a model/trust-region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between a Gauss-Newton and an augmented Hessian approximation. Gauss-Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics.