A Fast, Flexible Algorithm for the Graph-Fused Lasso
<img src="https://github.com/tansey/gfl/blob/master/img/example1.png?raw=true" alt="Example GFL Solution"/>
The goal in the graph-fused lasso (GFL) is to find a solution to the following convex optimization problem:
<img src="https://github.com/tansey/gfl/blob/master/img/eq1.png?raw=true" alt="GFL Convex Optimization Problem"/>
where __l__ is a smooth, convex loss function. The problem assumes you are given a graph structure of edges and nodes, where each node corresponds to a variable and edges between nodes correspond to constraints on the first differences between the variables. The objective function then seeks to find a solution to the above problem that minimizes the loss function over the vertices plus the sum of the first differences defined by the set of edges __E__.
The solution implemented here is based on the graph-theoretic trail decomposition and ADMM algorithm implemented in . The code relies on a slightly modified version of a linear-time dynamic programming solution to the 1-d (i.e. chain) GFL .
The python (Python version 2) wrapper requires `numpy`, `scipy`, and `networkx` to be able to run everything.
Note that the `libgraphfl` library also depends on the [Gnu Scientific Library `gsl`](https://www.gnu.org/software/gsl/) which should be available on your system.
The package can be installed via Pip:
`pip install pygfl`
or directly from source:
python setup.py build
python setup.py install
Note that the installation has not been tested on anything other than Mac OS X and Ubuntu. The underlying solver is implemented in pure C and should be cross-platform compatible.
The simplest way to run the script is via the command-line `graphfl` script. You just give it a CSV of your data that you wish to smooth and a CSV of your edges, one edge per row:
graphfl example/data.csv example/edges.csv --o example/smoothed.csv
This will run a solution path to auto-tune the value of the penalty parameter (the λ in equation 1). The results will be saved in `example/smoothed.csv`. The results should look something like the image at the top of the readme.
Calling within Python
To call the solver within a Python program, the simplest way is to use the `easy.solve_gfl` method:
import numpy as np
from pygfl.easy import solve_gfl
# Load data and edges
y = np.loadtxt('path/to/data.csv', delimiter=',')
edges = np.loadtxt('/path/to/edges.csv', delimiter=',', dtype=int)
# Run the solver
beta = solve_gfl(y, edges)
There are lots of other configuration options that affect the optimization procedure, but honestly they make little practical difference for most people.
Compiling the C solver lib separately
To compile the C solver as a standalone library, you just need to run the make file from the `cpp` directory:
Then you will need to make sure that you have the `cpp/lib` directory in your `LD_LIBRARY_PATH`:
Note the above instructions are for *nix users.
This library / package is distributed under the GNU Lesser General Public License, version 3. Note that a subset of code from  was modified and is included in the C source.
 W. Tansey and J. G. Scott. "[A Fast and Flexible Algorithm for the Graph-Fused Lasso](http://arxiv.org/abs/1505.06475)," arXiv:1505.06475, May 2015.
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