Class GradientDescent

source code

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

The gradient descent algorithm.

Parameters
----------
eps : Positive float. Tolerance for the stopping criterion.

info : List or tuple of utils.consts.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 20000.

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.gradient import GradientDescent
>>> from parsimony.functions.losses import RidgeRegression
>>> import numpy as np
>>> np.random.seed(42)
>>> X = np.random.rand(100, 50)
>>> y = np.random.rand(100, 1)
>>> gd = GradientDescent(max_iter=10000)
>>> function = RidgeRegression(X, y, k=0.0, mean=False)
>>> beta1 = gd.run(function, np.random.rand(50, 1))
>>> beta2 = np.dot(np.linalg.pinv(X), y)
>>> round(np.linalg.norm(beta1 - beta2), 13)
0.0003121557633

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

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

beta : Numpy array. The start vector.