Package parsimony :: Package functions :: Module losses :: Class LinearRegression

Class LinearRegression

                        object --+        
                                 |        
               properties.Function --+    
                                     |    
          properties.CompositeFunction --+
                                         |
                            object --+   |
                                     |   |
                   properties.Gradient --+
                                         |
                            object --+   |
                                     |   |
properties.LipschitzContinuousGradient --+
                                         |
                            object --+   |
                                     |   |
                   properties.StepSize --+
                                         |
                                        LinearRegression

The Linear regression loss function.

Instance Methods

[hide private]

__init__(self, X, y, mean=True)
Parameters ---------- X : Numpy array (n-by-p).

source code

reset(self)
Free any cached computations from previous use of this Function.

source code

f(self, beta)
Function value.

source code

grad(self, beta)
Gradient of the function at beta.

source code

L(self)
Lipschitz constant of the gradient.

source code

step(self, beta, index=0)
The step size to use in descent methods.

source code

Inherited from properties.Function: get_params, set_params

Inherited from properties.Gradient: approx_grad

Inherited from properties.LipschitzContinuousGradient: approx_L

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Class Variables

[hide private]

__abstractmethods__ = frozenset([])

Inherited from properties.CompositeFunction: __metaclass__

Inherited from properties.Function (private): _abc_cache, _abc_negative_cache, _abc_negative_cache_version, _abc_registry

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, X, y, mean=True)
(Constructor)

source code


Parameters
----------
X : Numpy array (n-by-p). The regressor matrix.

y : Numpy array (n-by-1). The regressand vector.

k : Non-negative float. The ridge parameter.

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

Overrides: object.__init__

reset(self)

source code

Free any cached computations from previous use of this Function.

From the interface "Function".

Overrides: properties.Function.reset

f(self, beta)

source code

Function value.

From the interface "Function".

Parameters
----------
beta : Numpy array. Regression coefficient vector. The point at which
        to evaluate the function.

Overrides: properties.Function.f

grad(self, beta)

source code

Gradient of the function at beta.

From the interface "Gradient".

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

Examples
--------
>>> import numpy as np
>>> from parsimony.functions.losses import LinearRegression
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(100, 150)
>>> y = np.random.rand(100, 1)
>>> lr = LinearRegression(X=X, y=y)
>>> beta = np.random.rand(150, 1)
>>> round(np.linalg.norm(lr.grad(beta)
...       - lr.approx_grad(beta, eps=1e-4)), 9)
1.3e-08

Overrides: properties.Gradient.grad

L(self)

source code

Lipschitz constant of the gradient.

From the interface "LipschitzContinuousGradient".

Examples
--------
>>> import numpy as np
>>> from parsimony.functions.losses import LinearRegression
>>>
>>> np.random.seed(42)
>>> X = np.random.rand(10, 15)
>>> y = np.random.rand(10, 1)
>>> lr = LinearRegression(X=X, y=y)
>>> L = lr.L()
>>> L_ = lr.approx_L((15, 1), 10000)
>>> L >= L_
True
>>> round((L - L_) / L, 14)
0.14039091870818

Overrides: properties.LipschitzContinuousGradient.L

step(self, beta, index=0)

source code

The step size to use in descent methods.

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

Overrides: properties.StepSize.step

Class LinearRegression

__init__(self, X, y, mean=True) (Constructor)

reset(self)

f(self, beta)

grad(self, beta)

L(self)

step(self, beta, index=0)

init(self, X, y, mean=True)
(Constructor)