rexjz / group-lasso

Group Lasso implementation following the scikit-learn API

Group Lasso

The group lasso [1] regulariser is a well known method to achieve structured sparsity in machine learning and statistics. The idea is to create non-overlapping groups of covariates, and recover regression weights in which only a sparse set of these covariate groups have non-zero components.

There are several reasons for why this might be a good idea. Say for example that we have a set of sensors and each of these sensors generate five measurements. We don't want to maintain an unneccesary number of sensors. If we try normal LASSO regression, then we will get sparse components. However, these sparse components might not correspond to a sparse set of sensors, since they each generate five measurements. If we instead use group LASSO with measurements grouped by which sensor they were measured by, then we will get a sparse set of sensors.

An extension of the group lasso regulariser is the sparse group lasso regulariser [2], which imposes both group-wise sparsity and coefficient-wise sparsity. This is done by combining the group lasso penalty with the traditional lasso penalty. In this library, I have implemented an efficient sparse group lasso solver being fully scikit-learn API compliant.

About this project

This project is developed by Yngve Mardal Moe and released under an MIT lisence.

Installation guide

Group-lasso requires Python 3.5+, numpy and scikit-learn. To install group-lasso via pip, simply run the command:

pip install group-lasso

Alternatively, you can manually pull this repository and run the setup.py file:

git clone https://github.com/yngvem/group-lasso.git
cd group-lasso
python setup.py

Documentation

You can read the full documentation on readthedocs.

Examples

There are several examples that show usage of the library here.

Further work

1. Fully test with sparse arrays and make examples
2. Make it easier to work with categorical data
3. Poisson regression

Implementation details

The problem is solved using the FISTA optimiser [3] with a gradient-based adaptive restarting scheme [4]. No line search is currently implemented, but I hope to look at that later.

Although fast, the FISTA optimiser does not achieve as low loss values as the significantly slower second order interior point methods. This might, at first glance, seem like a problem. However, it does recover the sparsity patterns of the data, which can be used to train a new model with the given subset of the features.

Also, even though the FISTA optimiser is not meant for stochastic optimisation, it has to my experience not suffered a large fall in performance when the mini batch was large enough. I have therefore implemented mini-batch optimisation using FISTA, and thus been able to fit models based on data with ~500 columns and 10 000 000 rows on my moderately priced laptop.

Finally, we note that since FISTA uses Nesterov acceleration, is not a descent algorithm. We can therefore not expect the loss to decrease monotonically.

References

[1]	Yuan, M. and Lin, Y. (2006), Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68: 49-67. doi:10.1111/j.1467-9868.2005.00532.x

[2]	Simon, N., Friedman, J., Hastie, T., & Tibshirani, R. (2013). A sparse-group lasso. Journal of Computational and Graphical Statistics, 22(2), 231-245.

[3]	Beck, A. and Teboulle, M. (2009), A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences 2009 2:1, 183-202. doi:10.1137/080716542

[4]	O’Donoghue, B. & Candès, E. (2015), Adaptive Restart for Accelerated Gradient Schemes. Found Comput Math 15: 715. doi:10.1007/s10208-013-9150-