- Predicting Correlation of Bagging Estimators in Logistic Regression
- Project Year:
2023
- REU Student (s):
Iris Chang | Columbia University in the City of New York NY
- Student 1 Institution:
Columbia University in the City of New York
- Project Mentor:
Pierre Bellec
- Project Mentor Area:
Statistics
- Project Abstract:
Logistic regression is used to make a prediction between two different outcomes based on a data set. Typically, when the sample size is much larger compared to a fixed dimension, maximum likelihood estimation is used to estimate the parameters of the model, in which case the estimate has many convenient properties such as being unbiased. It was shown by Sur and Candes (2018) as well as Salehi et al. (2019) that these assumptions do not hold in the high dimensional regime where the sample size and dimension are proportional. While these two groups were able to find adequate methods of characterizing model performance in high dimensions, there is an absence of work on the performance and impact of bagging on high dimensional logistic regression models. In our case, bagging refers to the method of dividing the larger data set into two or more overlapping subsets and fitting a logistic regression model on each subset before aggregating the parts together. This work aims to show a single scalar that would be able to predict the correlation between the two unaggregated estimates. Drawing from previous results in linear regression and the unbagged setting, we were able to successfully infer this result.
