def feed_forward(X, theta, n_hidden_layers=1):
"""Applies forward propagation to calculate model's hypothesis.
Args:
X (numpy.array): Features' dataset.
theta (numpy.array): Column vector of model's parameters.
n_hidden_layers (int): Number of hidden layers in network.
Returns:
(numpy.array(numpy.array), numpy.array(numpy.array)): A 2-tuple
consisting of an array of parameters prior to activation by layer
and an array of activation matrices by layer.
"""
z = empty((n_hidden_layers + 2), dtype=object)
a = empty((n_hidden_layers + 2), dtype=object)
# Input layer
a[0] = X
# Hidden unit layers
for l in range(1, (len(a) - 1)):
z[l] = a[l - 1].dot(theta[l - 1].T)
a[l] = g(z[l])
a[l] = append(
ones((len(a[l]), 1), float64), # add intercept
a[l],
axis=1)
# Output layer
z[len(a) - 1] = a[(len(a) - 2)].dot(theta[(len(a) - 2)].T)
a[len(a) - 1] = g(z[len(a) - 1]) # hypothesis
return z, a
def h(X, w, b):
"""Logistic regression hypothesis.
Args:
X (numpy.array): Transposed features' dataset.
w (numpy.array): Column vector of model's parameters.
b (float): Model's intercept parameter.
Returns:
numpy.array: The probability that each entry belong to class 1.
"""
return g(dot(w.T, X) + b)
def feed_forward(X, theta, n_hidden_layers=1):
"""Applies forward propagation to calculate model's hypothesis.
:param X: Features' dataset.
:type X: numpy.array
:param theta: Column vector of model's parameters.
:type theta: numpy.array
:param n_hidden_layers: Number of hidden layers in network.
:type n_hidden_layers: int
:returns:
- z - array of parameters prior to activation by layer.
- a - array of activation matrices by layer.
:rtype:
- z (:py:class: numpy.array(numpy.array))
- a (:py:class: numpy.array(numpy.array))
"""
z = empty((n_hidden_layers + 2), dtype=object)
a = empty((n_hidden_layers + 2), dtype=object)
# Input layer
a[0] = X
# Hidden unit layers
for l in range(1, (len(a) - 1)):
z[l] = a[l - 1].dot(theta[l - 1].T)
a[l] = g(z[l])
a[l] = append(
ones((len(a[l]), 1), float64), # add intercept
a[l],
axis=1)
# Output layer
z[len(a) - 1] = a[(len(a) - 2)].dot(theta[(len(a) - 2)].T)
a[len(a) - 1] = g(z[len(a) - 1]) # hypothesis
return z, a
def h(X, theta):
"""Logistic regression hypothesis.
Args:
X (numpy.array): Features' dataset plus bias column.
theta (numpy.array): Column vector of model's parameters.
Raises:
ValueError
Returns:
numpy.array: The probability that each entry belong to class 1.
"""
return g(X.dot(theta))
def predict_prob(X, theta):
"""Produces the probability that the entries belong to class 1.
Returns:
X (numpy.array): Features' dataset plus bias column.
theta (numpy.array): Column vector of model's parameters.
Raises:
ValueError
Returns:
numpy.array: The probability that each entry belong to class 1.
"""
return g(X.dot(theta))
def h(X, theta):
"""Logistic regression hypothesis.
:param X: Features' dataset plus bias column.
:type X: numpy.array
:param theta: Column vector of model's parameters.
:type theta: numpy.array
:raises: ValueError
:returns: The probability that each entry belong to class 1.
:rtype: numpy.array
"""
return g(X.dot(theta))
def predict_prob(X, theta):
""" Produces the probability that the entries belong to class 1.
:param X: Features' dataset plus bias column.
:type X: numpy.array
:param theta: Column vector of model's parameters.
:type theta: numpy.array
:raises: ValueError
:returns: The probability that each entry belong to class 1.
:rtype: numpy.array
"""
return g(X.dot(theta))