Before revision:  While this (or any other) algorithm may fail to identify the structure of the underlying model correctly from a finite sample, we show that it will still learn a tree-structured model that is close to the true one in TV distance, a guarantee called "proper learning."
After revision:  While this (or any other) algorithm may fail to identify the structure of the underlying model correctly from a finite sample, we show that it will still learn a tree-structured model that is close to the true one in total variation distance, a guarantee called "proper learning."