Sherman-Morrison rank-one updates have been used successfully for adaptive sparse grid density estimation. This allowed for regularization and adaptivity, but until now, this has only been possible in the offline/online splitting context using an orthogonal decomposition, such as tridiagonal. The new approach studied in this paper generalizes the old version of the Sherman-Morrison formula based sparse grid density estimation by using the Sherman-Morrison-Woodbury (SMW) formula. This allows for arbitrary decompositions in the offline phase and better supports parallelization by allowing for simultaneous adaptivity operations (rank-k updates), while keeping all features, such as regularization in between off/on phases. A parallelized/distributed version of the new SMW approach has been implemented and evaluated against the old version, and shows enhancements in terms of speed, while keeping the accuracy. It scales well for reasonably sized rank-k updates.     «

Sherman-Morrison rank-one updates have been used successfully for adaptive sparse grid density estimation. This allowed for regularization and adaptivity, but until now, this has only been possible in the offline/online splitting context using an orthogonal decomposition, such as tridiagonal. The new approach studied in this paper generalizes the old version of the Sherman-Morrison formula based sparse grid density estimation by using the Sherman-Morrison-Woodbury (SMW) formula. This allows for...     »