Uncertainty Quantification in Logistic Regression using Random Fuzzy Sets and Belief Functions

Uncertainty Quantification in Logistic Regression using Random Fuzzy Sets and Belief Functions

2024 | Thierry Denœux
This paper explores the application of evidential likelihood-based inference to logistic regression, particularly in binomial and multinomial cases. The approach uses random fuzzy sets and belief functions to quantify uncertainty in logistic regression models. In the binomial case, the predictive belief function is computed by numerically integrating the possibility distribution of the posterior probability. For multinomial cases, the solution involves a combination of constrained nonlinear optimization and Monte Carlo simulation. Both methods can be simplified using a normal approximation to the relative likelihood function. Numerical experiments show that decision rules based on predictive belief functions outperform those based on posterior probabilities in terms of error rates for different rejection rates. The paper also discusses the extension of the method to multinomial classification and provides examples to illustrate the theoretical concepts and computational procedures.This paper explores the application of evidential likelihood-based inference to logistic regression, particularly in binomial and multinomial cases. The approach uses random fuzzy sets and belief functions to quantify uncertainty in logistic regression models. In the binomial case, the predictive belief function is computed by numerically integrating the possibility distribution of the posterior probability. For multinomial cases, the solution involves a combination of constrained nonlinear optimization and Monte Carlo simulation. Both methods can be simplified using a normal approximation to the relative likelihood function. Numerical experiments show that decision rules based on predictive belief functions outperform those based on posterior probabilities in terms of error rates for different rejection rates. The paper also discusses the extension of the method to multinomial classification and provides examples to illustrate the theoretical concepts and computational procedures.
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[slides and audio] Uncertainty quantification in logistic regression using random fuzzy sets and belief functions