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SLEP: A Sparse Learning Package

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The SLEP (Sparse Learning with Efficient Projections) package provides a set of programs for sparse learning:

L₁-regularized (constrained) sparse learning

The L₁-regularized sparse learning problem has the following general form:

min_x f(x) + λ||x||₁

Here f(.) is a convex, but not necessarily strictly convex, function, x is a vector of length n, and λ>0 is a regularization parameter.

L₁/L_q-regularized sparse learning (q>1)

The L₁/L_q-regularized sparse learning problem has the following general form:

min_x f(x) + λ ||x||_q,1

Here f(.) is a convex, but not necessarily strictly convex, function, λ>0 is a regularization parameter, and the (q,1)-norm of x is based on a (predefined) partitioning of x into a set of non-overlapping groups.

Trace norm regularized learning

The trace norm regularized learning problem has the following general form:

min_x f(X) + λ ||X||_*

Here f(.) is a convex, but not necessarily strictly convex, function, X is a matrix of size n by k, λ>0 is a regularization parameter, and the trace norm of X denoted as ||X||_* is defined as the summation of its singular values.

Loss Function

In the current version, we implement the following two loss functions: (1) the least squares loss and (2) the logistic loss.

Acknowledgements

The SLEP software project has been supported by research grants from the NSF and National Geospatial-Intelligence Agency.

If you have any suggestions or you have found a bug, please contact us via email at j.liu@asu.edu or jieping.ye@asu.edu.