Class LatentVariableVariance

x.__init__(...) initializes x; see help(type(x)) for signature

Overrides: object.__init__

(inherited documentation)

Free any cached computations from previous use of this Function.

Overrides: properties.Function.reset

(inherited documentation)

Function value.

From the interface "Function".

Examples
--------
>>> import numpy as np
>>> from parsimony.algorithms.nipals import FastSVD
>>> from parsimony.functions.losses import LatentVariableVariance
>>>
>>> np.random.seed(1337)
>>> X = np.random.rand(50, 150)
>>> w = np.random.rand(150, 1)
>>> var = LatentVariableVariance(X)
>>> round(var.f(w), 12)
-1295.854475188615
>>> round(-np.dot(w.T, np.dot(X.T, np.dot(X, w)))[0, 0] / 49.0, 12)
-1295.854475188615

Overrides: properties.Function.f

Gradient of the function.

From the interface "Gradient".

Parameters
----------
w : The point at which to evaluate the gradient.

Examples
--------
>>> import numpy as np
>>> from parsimony.functions.losses import LatentVariableVariance
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(50, 150)
>>> var = LatentVariableVariance(X)
>>> w = np.random.rand(150, 1)
>>> np.linalg.norm(var.grad(w) - var.approx_grad(w, eps=1e-4)) < 5e-8
True

Overrides: properties.Gradient.grad

Lipschitz constant of the gradient with given index.

From the interface "LipschitzContinuousGradient".

Examples
--------
>>> import numpy as np
>>> from parsimony.algorithms.nipals import FastSVD
>>> from parsimony.functions.losses import LatentVariableVariance
>>>
>>> np.random.seed(1337)
>>> X = np.random.rand(50, 150)
>>> w = np.random.rand(150, 1)
>>> var = LatentVariableVariance(X)
>>> round(var.L(), 10)
47025.0809786841
>>> _, S, _ = np.linalg.svd(np.dot(X.T, X))
>>> round(np.max(S) * 49 / 2.0, 10)
47025.0809786841

Overrides: properties.LipschitzContinuousGradient.L

The step size to use in descent methods.

Parameters
----------
w : Numpy array. The point at which to determine the step size.

Examples
--------
>>> import numpy as np
>>> from parsimony.algorithms.nipals import FastSVD
>>> from parsimony.functions.losses import LatentVariableVariance
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(50, 150)
>>> w = np.random.rand(150, 1)
>>> var = LatentVariableVariance(X)
>>> var.step(w)
2.1979627581251385e-05
>>> _, S, _ = np.linalg.svd(np.dot(X.T, X))
>>> round(1.0 / (np.max(S) * 49 / 2.0), 15)
2.1979627581e-05

Overrides: properties.StepSize.step