• The standard VB method ('Sparse full-covariance method') calculates an inverse of regularized input covariance matrix. When the input dimension becomes over several thousands, computational time becomes very long because computational time for inverse calculation increases as cubic power of input dimension.
• 'Sparse space-covariance method' uses sparse constraints only on the space dimension and it does not impose sparse constraints on temporal dimension using time embedding (: temporal dimension is not pruned). This algorithm calculates inverse of spatial covariance matrix and much faster than the standard method for time embedding representation.
• 'Sparse stepwise method' maximize the free energy coordinate by coordinate. This method does not use inverse covariance matrix. This method also introduce sparse condition only for spatial dimension but not for temporal dimension.
• 'Sparse sequential method' is a incremental method proposed by Tipping and Faul (2003). It increases effective input dimension one by one. This method introduce sparse condition both for space & time dimension. However, this method becomes slow for more than 10,000 total dimension.

Latest version
• SparseRegression (2011-11-11) (zip)
• MEX-program (2010-06-21) (zip)

Early version
• SparseRegression version 1.0 (zip)
• MEX-program (zip)

• unzip the zipped file to appropriate place
• Make MEX file
• run mex_compile at the directory mex_prog
• set path to the unzipped directory of this toolbox
• example script: set_path.m
• Run the Test program
• testjob;

Please see Usage-predict.txt and testjob.m for more detail on how to use this toolbox. Please see Read_embed.txt for time delay embedding representation. In the previous version, time delay embedding was done before estimation. When input dimension becomes very large, this requires huge amount of memory and time. Therefore, embedding was done inside the estimation program using MEX-program. SparseEstimation_intro.pdf

Sato M., (2001). On-line model selection based on the variational Bayes. Neural Computation, 13, 1649-1681.

Toda, A., Imamizu, H., Sato, M., Wada, Y., Kawato, M., (2007). Reconstruction of temporal movement from single-trial non-invasive brain activity: A hierarchical Bayesian method. The 14th International Conference on Neural Information Processing (ICONIP2007).

Isao Nambu, Rieko Osu, Masa-aki Sato, Soichi Ando, Mitsuo Kawato, Eiichi Naito, (2009). Single-trial reconstruction of finger-pinch forces from human motor-cortical activation measured by near-infrared spectroscopy (NIRS) NeuroImage 47, 628-637.

Tipping, M. E. and A. C. Faul, (2003). Fast marginal likelihood maximisation for sparse Bayesian models. In C. M. Bishop and B. J. Frey (Eds.), Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, Key West, FL, Jan 3-6.

The codes in the toolbox were written for MATLAB ver.6.5 or later. VBSR toolbox is free but copyright software, distributed under the terms of the GNU General Public License as published by the Free Software Foundation . Further details on GPL can be found at http://www.gnu.org/copyleft/. No formal support or maintenance is provided or implied. Masa-aki Sato
ATR Computational Neuroscience Laboratories
Department of Computational Brain Imaging