Multiresponce Sparse Regression

hpelm.modules.mrsr.mrsr(X, T, kmax)[source]

Multiresponse Sparse Regression (MRSR) algorithm in Python, accelerated by Numpy.

Finds most relevant inputs for a regression problem with multiple outputs, returns these inputs one-by-one. Fast implementation, but has complexity O(2^m) for m features in output.

Parameters:
  • T (matrix) – an (n x p) matrix of targets. The columns of T should have zero mean and same scale (e.g. equal variance).
  • X (matrix) – an (n x m) matrix of regressors. The columns of X should have zero mean and same scale (e.g. equal variance).
  • kmax (int) – an integer fixing the number of steps to be run, which equals to the maximum number of regressors in the model.
Returns:

i1 – a (1 x kmax) vector of indices revealing the order in which the regressors enter model.
Return type:

vector
Reference:
Timo Simila, Jarkko Tikka. Multiresponse sparse regression with application to multidimensional scaling. International Conference on Artificial Neural Networks (ICANN). Warsaw, Poland. September 11-15, 2005. LNCS 3697, pp. 97-102.

Multiresponce Sparse Regression v2

hpelm.modules.mrsr2.mrsr2(X, T, kmax, norm=2)[source]

Multi-Responce Sparse Regression implementation with linear scaling in number of outputs.

Basically an L1-regularized regression with multiple outputs, regularization considers all outputs together, method returns the best input features one by one and can be stopped early. Compared to an original MRSR this method is slower for small problems, but has a linear complexity in the number of outputs instead of exponential one, so it is suitable for auto-encoders and other tasks with large output dimensionality.

Parameters:
  • T (matrix) – an (n x p) matrix of targets. The columns of T should have zero mean and same scale (e.g. equal variance).
  • X (matrix) – an (n x m) matrix of regressors. The columns of X should have zero mean and same scale (e.g. equal variance).
  • kmax (int) – an integer fixing the number of steps to be run, which equals to the maximum number of regressors in the model.
  • norm (from Numpy.linalg.norm) – norm to use in MRSR2, can be 1 for L1 or 2 for L2 norm, default 2.
Returns:

i1 – a (1 x kmax) vector of indices revealing the order in which the regressors enter model.
Return type:

vector
Reference:
Better MRSR implementation according to: “Common subset selection of inputs in multiresponse regression” by Timo Similä and Jarkko Tikka, International Joint Conference on Neural Networks 2006

Created on Sun Jan 26 13:48:54 2014 @author: Anton Akusok