Gradient boosting decision tree implementation I am willing to implement my own GBM. I have been looking - unsuccessfully - for a clear article describing the implementation of gradient boosting machine for decision trees. Sources like this are too general and do not provide implementation details.
I am especially interested in sparse data sets and algorithmic optimizations that I may use in this specific case.
 A: I'm not sure if you're looking for a mathematical implementation or a code one, but assuming the latter (and that you're using Python) sklearn has two implementations of a gradient boosted decision tree. One for regression and one for classification. 
http://scikit-learn.org/stable/modules/ensemble.html#gradient-tree-boosting
They have a couple of simple examples there, but if you google sklearn gradient boosting there are tons of examples/tutorials out there. 
As for a sparse data set I'm not sure what to tell you. There's some optional parameters when creating the boosted tree but I'm not sure any of them would help with that. If you use a random forest you can create class weights which I've found useful in unbalanced data sets.
A: I do not know whether you found anything yet, but here is a blog post with a great  explanation on "Gradient Boosting from scratch" link.
Within the same post there is a link to the full Python implementation of Gradient Boosting Trees link.
Also a very similar post going deeper into Tree Boosting With XGBoost with lost of details link.
Hope these help. 
