neupy.algorithms.gd.quasi_newton module

class neupy.algorithms.gd.quasi_newton.QuasiNewton[source]

Quasi-Newton algorithm. Every iteration quasi-Network method approximates inverse Hessian matrix with iterative updates. It doesn’t have step parameter. Instead, algorithm applies line search for the step parameter that satisfies strong Wolfe condition. Parameters that control wolfe search start with the wolfe_ prefix.

Parameters:

update_function : bfgs, dfp, sr1

Update function for the iterative inverse hessian matrix approximation. Defaults to bfgs.

  • bfgs - It’s rank 2 formula update. It can suffer from round-off error and inaccurate line searches.
  • dfp - DFP is a method very similar to BFGS. It’s rank 2 formula update. It can suffer from round-off error and inaccurate line searches.
  • sr1 - Symmetric rank 1 (SR1). Generates update for the inverse hessian matrix adding symmetric rank-1 matrix. It’s possible that there is no rank 1 updates for the matrix and in this case update won’t be applied and original inverse hessian will be returned.

h0_scale : float

Default Hessian matrix is an identity matrix. The h0_scale parameter scales identity matrix. Defaults to 1.

epsilon : float

Controls numerical stability for the update_function parameter. Defaults to 1e-7.

wolfe_maxiter : int

Controls maximun number of iteration during the line search that identifies optimal step size during the weight update stage. Defaults to 20.

wolfe_c1 : float

Parameter for Armijo condition rule. It’s used during the line search that identifies optimal step size during the weight update stage. Defaults 1e-4.

wolfe_c2 : float

Parameter for curvature condition rule. It’s used during the line search that identifies optimal step size during the weight update stage. Defaults 0.9.

connection : list, tuple or LayerConnection instance

Network’s architecture. There are a few ways to define it.

  • List of layers. For instance, [Input(2), Tanh(4), Relu(1)].
  • Construct layer connections. For instance, Input(2) > Tanh(4) > Relu(1).
  • Tuple of integers. Each integer defines Sigmoid layer and it’s input size. For instance, value (2, 4, 1) means that network has 3 layers with 2 input units, 4 hidden units and 1 output unit.

error : str or function

Error/loss function. Defaults to mse.

  • mae - Mean Absolute Error.
  • mse - Mean Squared Error.
  • rmse - Root Mean Squared Error.
  • msle - Mean Squared Logarithmic Error.
  • rmsle - Root Mean Squared Logarithmic Error.
  • categorical_crossentropy - Categorical cross entropy.
  • binary_crossentropy - Binary cross entropy.
  • binary_hinge - Binary hinge entropy.
  • categorical_hinge - Categorical hinge entropy.
  • Custom function which accepts two mandatory arguments. The first one is expected value and the second one is predicted value. Example:
def custom_func(expected, predicted):
    return expected - predicted

show_epoch : int or str

This property controls how often the network will display information about training. There are two main syntaxes for this property.

  • You can define it as a positive integer number. It defines how offen would you like to see summary output in terminal. For instance, number 100 mean that network shows summary at 100th, 200th, 300th ... epochs.
  • String defines number of times you want to see output in terminal. For instance, value '2 times' mean that the network will show output twice with approximately equal period of epochs and one additional output would be after the finall epoch.

Defaults to 1.

shuffle_data : bool

If it’s True class shuffles all your training data before training your network, defaults to True.

epoch_end_signal : function

Calls this function when train epoch finishes.

train_end_signal : function

Calls this function when train process finishes.

verbose : bool

Property controls verbose output interminal. True enables informative output in the terminal and False - disable it. Defaults to False.

addons : list or None

The list of addon algortihms. None by default. If this option is not empty it will generate new class which will inherit all from this list. Support two types of addon algorithms: weight update and step update.

Notes

  • Method requires all training data during propagation, which means it’s not allowed to use mini-batches.

References

[1] Yang Ding, Enkeleida Lushi, Qingguo Li,
Investigation of quasi-Newton methods for unconstrained optimization. http://people.math.sfu.ca/~elushi/project_833.pdf
[2] Jorge Nocedal, Stephen J. Wright, Numerical Optimization.
Chapter 6, Quasi-Newton Methods, p. 135-163

Examples

>>> import numpy as np
>>> from neupy import algorithms
>>>
>>> x_train = np.array([[1, 2], [3, 4]])
>>> y_train = np.array([[1], [0]])
>>>
>>> qnnet = algorithms.QuasiNewton(
...     (2, 3, 1),
...     update_function='bfgs'
... )
>>> qnnet.train(x_train, y_train, epochs=10)

Attributes

errors (ErrorHistoryList) Contains list of training errors. This object has the same properties as list and in addition there are three additional useful methods: last, previous and normalized.
train_errors (ErrorHistoryList) Alias to the errors attribute.
validation_errors (ErrorHistoryList) The same as errors attribute, but it contains only validation errors.
last_epoch (int) Value equals to the last trained epoch. After initialization it is equal to 0.

Methods

predict(input_data) Predicts output for the specified input.
train(input_train, target_train, input_test=None, target_test=None, epochs=100, epsilon=None) Train network. You can control network’s training procedure with epochs and epsilon parameters. The input_test and target_test should be presented both in case of you need to validate network’s training after each iteration.
fit(*args, **kwargs) Alias to the train method.
epsilon = None[source]
h0_scale = None[source]
init_train_updates()[source]

Initialize updates that would be applied after each training epoch.

init_variables()[source]

Initialize Tensorflow variables.

options = {'verbose': Option(class_name='Verbose', value=VerboseProperty(name="verbose")), 'show_epoch': Option(class_name='BaseNetwork', value=ShowEpochProperty(name="show_epoch")), 'shuffle_data': Option(class_name='BaseNetwork', value=Property(name="shuffle_data")), 'epoch_end_signal': Option(class_name='BaseNetwork', value=Property(name="epoch_end_signal")), 'train_end_signal': Option(class_name='BaseNetwork', value=Property(name="train_end_signal")), 'error': Option(class_name='ConstructibleNetwork', value=FunctionWithOptionsProperty(name="error")), 'addons': Option(class_name='BaseGradientDescent', value=Property(name="addons")), 'wolfe_maxiter': Option(class_name='WolfeLineSearchForStep', value=IntProperty(name="wolfe_maxiter")), 'wolfe_c1': Option(class_name='WolfeLineSearchForStep', value=NumberProperty(name="wolfe_c1")), 'wolfe_c2': Option(class_name='WolfeLineSearchForStep', value=NumberProperty(name="wolfe_c2")), 'update_function': Option(class_name='QuasiNewton', value=ChoiceProperty(name="update_function")), 'epsilon': Option(class_name='QuasiNewton', value=NumberProperty(name="epsilon")), 'h0_scale': Option(class_name='QuasiNewton', value=NumberProperty(name="h0_scale"))}[source]
step = None[source]
update_function = None[source]