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A Fast, Flexible Algorithm for the Graph-Fused Lasso

----------------------------------------------------

<p align="center">

<img src="https://github.com/tansey/gfl/blob/master/img/example1.png?raw=true" alt="Example GFL Solution"/>

</p>

The goal in the graph-fused lasso (GFL) is to find a solution to the following convex optimization problem:

<p align="center">

<img src="https://github.com/tansey/gfl/blob/master/img/eq1.png?raw=true" alt="GFL Convex Optimization Problem"/>

</p>

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 [1]. The code relies on a slightly modified version of a linear-time dynamic programming solution to the 1-d (i.e. chain) GFL [2].

Python Requirements

===================

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.

Installing

==========

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.

Running

=======

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:

`make all`

Then you will need to make sure that you have the `cpp/lib` directory in your `LD_LIBRARY_PATH`:

`export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/my/path/to/gfl/cpp/lib/`

Note the above instructions are for *nix users.

Licensing

=========

This library / package is distributed under the GNU Lesser General Public License, version 3. Note that a subset of code from [2] was modified and is included in the C source.

References

==========

[1] 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.

[2] [glmgen](https://github.com/statsmaths/glmgen)

----------------------------------------------------

<p align="center">

<img src="https://github.com/tansey/gfl/blob/master/img/example1.png?raw=true" alt="Example GFL Solution"/>

</p>

The goal in the graph-fused lasso (GFL) is to find a solution to the following convex optimization problem:

<p align="center">

<img src="https://github.com/tansey/gfl/blob/master/img/eq1.png?raw=true" alt="GFL Convex Optimization Problem"/>

</p>

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 [1]. The code relies on a slightly modified version of a linear-time dynamic programming solution to the 1-d (i.e. chain) GFL [2].

Python Requirements

===================

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.

Installing

==========

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.

Running

=======

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:

`make all`

Then you will need to make sure that you have the `cpp/lib` directory in your `LD_LIBRARY_PATH`:

`export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/my/path/to/gfl/cpp/lib/`

Note the above instructions are for *nix users.

Licensing

=========

This library / package is distributed under the GNU Lesser General Public License, version 3. Note that a subset of code from [2] was modified and is included in the C source.

References

==========

[1] 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.

[2] [glmgen](https://github.com/statsmaths/glmgen)

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