An efficient implementation for the MPGL method (a matching pursuit method for generalized LASSO problem) in the paper:
MPGL: An Efficient Matching Pursuit Method for Generalized LASSO
Dong Gong, Mingkui Tan, Yanning Zhang, Anton van den Hengel, Qinfeng Shi.
In Thirty-First AAAI Conference on Artificial Intelligence (AAAI), 2017.
[Paper][Project]

• If you use this code for your research, please cite our paper:

@inproceedings{gong2017mpgl,
  title={MPGL: An Efficient Matching Pursuit Method for Generalized LASSO},
  author={Gong, Dong and Tan, Mingkui and Zhang, Yanning and van den Hengel, Anton and Shi, Qinfeng},
  booktitle={AAAI Conference on Artificial Intelligence},
  year={2017}
}

• This implementation is based on MATLAB and C++ with an MEX interface. The main framework and the entry of the algorithm is implemented in MATLAB. The most time consuming core part is implemented in C++ with MEX interface for high efficiency. An external library OpenBLAS is required.

• As shown in our paper, the MPGL algorithm and this implementation is both efficient and effective for many applications related to the generalized LASSO problem.

• Download the source to your/openblas/path/;
• Run Make;
• Copy the required .h files (i.e. cblas.h and openblas_config.h) to the mpgl/mxsolver/.
• This instruction is for Linux and OSX.
• More details for compiling and installation of OpenBLAS can be found from https://github.com/xianyi/OpenBLAS.

• Set openblas_path = 'your/openblas/path/' in makemexfiles.m;
• Run makemexfiles in MATLAB and get the .mex* files.
• We also provide a package with the compiled mex files.

• Run script_gendata to generate synthetic data for testing.
• The entry of the MPGL method is in entry_mpgl.m.
• Please find the instructions for tuning the parameters for data generation and MPGL in the comments in the .m files.

• This implementation mainly focuses on the model y=Ax+n and the generalized LASSO problem.
• The solver for the general case of A is in the mpgl/solver_ls/.
• For the cases with A=I (i.e. A is an identity matrix, FLSA problem or projection problem), we specifically provide an implementation to accelerate the computation. The related solver is in mpgl/solver_proj/.
• The core parts of the solver in C++ are in mpgl/mexsolver/.

To be updated...