Class StaticCONESTA

source code

            object --+        
                     |        
   bases.BaseAlgorithm --+    
                         |    
   bases.ExplicitAlgorithm --+
                             |
                object --+   |
                         |   |
  bases.IterativeAlgorithm --+
                             |
                object --+   |
                         |   |
bases.InformationAlgorithm --+
                             |
                            StaticCONESTA

COntinuation with NEsterov smoothing in a Soft-Thresholding Algorithm,
or CONESTA for short, with a statically decreasing sequence of eps and mu.

Parameters
----------
mu_min : Non-negative float. A "very small" mu to use as a lower bound for
        mu.

tau : Float, 0 < tau < 1. The rate at which eps is decreasing. Default
        is 0.5.

exponent : Float, in [1.001, 2.0]. The assumed convergence rate of
        ||beta* - beta_k||_2 for k=1,2,... is O(1 / k^exponent). Default
        is 1.5.

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.

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

Example
-------
>>> from parsimony.algorithms.proximal import StaticCONESTA
>>> from parsimony.functions.nesterov import l1tv
>>> from parsimony.functions import LinearRegressionL1L2TV
>>> import scipy.sparse as sparse
>>> import numpy as np
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(100, 50)
>>> y = np.random.rand(100, 1)
>>> A = sparse.csr_matrix((50, 50))  # Unused here
>>> function = LinearRegressionL1L2TV(X, y, 0.0, 0.0, 0.0,
...                                   A=[A], mu=0.0)
>>> static_conesta = StaticCONESTA(max_iter=10000)
>>> beta1 = static_conesta.run(function, np.random.rand(50, 1))
>>> beta2 = np.dot(np.linalg.pinv(X), y)
>>> round(np.linalg.norm(beta1 - beta2), 13)
3.0183961e-06
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(100, 50)
>>> y = np.random.rand(100, 1)
>>> A = sparse.csr_matrix((50, 50))
>>> function = LinearRegressionL1L2TV(X, y, 0.1, 0.0, 0.0,
...                                   A=[A], mu=0.0)
>>> static_conesta = StaticCONESTA(max_iter=10000)
>>> beta1 = static_conesta.run(function, np.random.rand(50, 1))
>>> beta2 = np.dot(np.linalg.pinv(X), y)
>>> round(np.linalg.norm(beta1 - beta2), 13)
0.8272329573827
>>> np.linalg.norm(beta2.ravel(), 0)
50
>>> np.linalg.norm(beta1.ravel(), 0)
7
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(100, 50)
>>> y = np.random.rand(100, 1)
>>> A = l1tv.linear_operator_from_shape((1, 1, 50), 50)
>>> function = LinearRegressionL1L2TV(X, y, 0.1, 0.1, 0.1,
...                                   A=A, mu=0.0)
>>> static_conesta = StaticCONESTA(max_iter=10000)
>>> beta1 = static_conesta.run(function, np.zeros((50, 1)))
>>> beta2 = np.dot(np.linalg.pinv(X), y)
>>> round(np.linalg.norm(beta1 - beta2), 13)
0.9662907379987

This function obtains a minimiser of a give function.

Parameters
----------
function : The function to minimise.

x : A starting point.