Class ShootingAlgorithm

source code

            object --+        
                     |        
   bases.BaseAlgorithm --+    
                         |    
   bases.ImplicitAlgorithm --+
                             |
                object --+   |
                         |   |
  bases.IterativeAlgorithm --+
                             |
                object --+   |
                         |   |
bases.InformationAlgorithm --+
                             |
                            ShootingAlgorithm

The shooting algorithm for the lasso.

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

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

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.

eps : Positive float. Tolerance for the stopping criterion.

info : List or tuple of utils.Info. What, if any, extra run information
        should be stored. Default is an empty list, which means that no
        run information is computed nor returned.

max_iter : Non-negative integer. Maximum allowed number of iterations.
        Default is 10000.

min_iter : Non-negative integer less than or equal to max_iter. Minimum
        number of iterations that must be performed. Default is 1.

Examples
--------
>>> from parsimony.algorithms.coordinate import ShootingAlgorithm
>>> import parsimony.functions as functions
>>> import parsimony.functions.penalties as penalties
>>> import numpy as np
>>> np.random.seed(42)
>>> X = np.random.rand(100, 50)
>>> beta_star = np.random.rand(50, 1)
>>> beta_star[beta_star < 0.5] = 0.0
>>> y = np.dot(X, beta_star) + 0.001 * np.random.randn(100, 1)
>>> l = 0.0618
>>> alg = ShootingAlgorithm(l)
>>> function = functions.CombinedFunction()
>>> function.add_function(functions.losses.LinearRegression(X, y,
...                                                         mean=False))
>>> function.add_prox(penalties.L1(l=l))
>>> beta = alg.run(X, y)
>>> round(np.linalg.norm(beta_star - beta), 14)
0.34655181469595

Find the minimiser of the associated function, starting at beta.

Parameters
----------
X : Numpy array, shape n-by-p. The matrix X with independent
        variables.

y : Numpy array, shape n-by-1. The response variable y.

beta : Numpy array. Optional starting point.