A Fast, Flexible Algorithm for the Graph-Fused Lasso
The goal in the graph-fused lasso (GFL) is to find a solution to the following 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
networkx to be able to run everything.
Note that the
libgraphfl library also depends on the Gnu Scientific Library
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
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
Then you will need to make sure that you have the
cpp/lib directory in your
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, O. Koyejo, R. A. Poldrack, and J. G. Scott. "False Discovery Rate Smoothing," Supplementary material. Journal of the American Statistical Association (JASA): Theory and Methods, June, 2017.