- Existence of the MLE in High-Dimensional Multinomial Logistic Regression
- Project Year:
2023
- REU Student (s):
Sumi Vora | Pomona College CA
- Student 1 Institution:
Pomona College
- Project Mentor:
Pierre Bellec
- Project Mentor Area:
Statistics
- Project Abstract:
Logistic regression is a supervised classification algorithm that predicts the probability of an event given a set of features. This technique relies on maximum likelihood estimation (MLE) to estimate the regression parameters for the log-odds of the observed data. The MLE, however, does not always exist. In particular, if there exists a linear decision boundary separating the classes, then the MLE will not converge. In 2018, Candes and Sur proved a theoretical phase transition curve for the existence of the MLE in binary logistic regression parametrized by the ratio of features to number of observations p/n and the norm of the regression coefficients. In our project, we are interested in finding an empirical and theoretical phase transition curve for the existence of the MLE in unregularized multinomial regression for K classes (K>2).
