def test_sigmoid_gradient(self):
z = array([-1, -0.5, 0, 0.5, 1])
assert_allclose(g_grad(z),
[0.196612, 0.235004, 0.25, 0.235004, 0.196612],
rtol=0,
atol=0.001,
equal_nan=False)
def back_propagation(y, theta, a, z, num_labels, n_hidden_layers=1):
"""Applies back propagation to minimize model's loss.
Args:
y (numpy.array): Column vector of expected values.
theta (numpy.array(numpy.array)): array of model's weight matrices by
layer.
a (numpy.array(numpy.array)): array of activation matrices by layer.
z (numpy.array(numpy.array)): array of parameters prior to sigmoid by
layer.
num_labels (int): Number of classes in multiclass classification.
n_hidden_layers (int): Number of hidden layers in network.
Returns:
numpy.array(numpy.array): array of matrices of 'error values' by layer.
"""
delta = empty((n_hidden_layers + 2), dtype=object)
L = n_hidden_layers + 1 # last layer
delta[L] = zeros(shape=a[L].shape, dtype=float64)
for c in range(num_labels):
delta[L][:, c] = a[L][:, c] - (y == c)
for l in range(L, 1, -1):
delta[l - 1] = delta[l].dot(theta[l - 1])[:, 1:] * g_grad(z[l - 1])
return delta