I used logistic regression on publicly available data to test dense vs. sparse classification. There are two datasets One is for Breast Cancer from Wisconsin. This is a dense dataset with n>p. The second dataset is about Coronary Artery Disease. It dataset is more sparse, but n>p still.
The code can be found in Dense vs Sparse Classification.ipynb and the interpretation of the output is in the Sparse vs Dense Classification.pdf and Sparse vs Dense Classification.pptx files.