Class Lasso

source code

     object --+        
              |        
  BaseEstimator --+    
                  |    
RegressionEstimator --+
                      |
                     Lasso

Linear regression with an L1 penalty:

    f(beta, X, y) = (1 / (2 * n)) * ||Xbeta - y||²_2 + l * ||beta||_1,

where ||.||_1 is the L1-norm.

Parameters
----------
l : Non-negative float. The Lagrange multiplier, or regularisation
        constant, of the function.

algorithm : ExplicitAlgorithm. The algorithm that should be applied.
        Should be one of:
            1. FISTA(...)
            2. ISTA(...)

        Default is FISTA(...).

algorithm_params : A dict. The dictionary algorithm_params contains
        parameters that should be set in the algorithm. Passing
        algorithm=FISTA(**params) is equivalent to passing
        algorithm=FISTA() and algorithm_params=params. Default is
        an empty dictionary.

start_vector : BaseStartVector. Generates the start vector that will be
        used.

penalty_start : Non-negative integer. The number of columns, variables
        etc., to be exempt from penalisation. Equivalently, the first
        index to be penalised. Default is 0, all columns are included.

mean : Boolean. Whether to compute the squared loss or the mean squared
        loss. Default is True, the mean squared loss.

Examples
--------
>>> import numpy as np
>>> import parsimony.estimators as estimators
>>> import parsimony.algorithms.proximal as proximal
>>> n = 10
>>> p = 16
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(n, p)
>>> y = np.random.rand(n, 1)
>>> l1 = 0.1  # L1 coefficient
>>> lasso = estimators.Lasso(l1,
...                          algorithm=proximal.FISTA(),
...                          algorithm_params=dict(max_iter=1000),
...                          mean=False)
>>> error = lasso.fit(X, y).score(X, y)
>>> print "error = ", error
error =  0.395494642796