def classification_error(output_vector,
target_vector,
axis=-1,
topN=1,
name=''):
'''
This operation computes the classification error. It finds the index of the highest
value in the output_vector and compares it to the actual ground truth label
(the index of the hot bit in the target vector). The result is a scalar
(i.e., one by one matrix). This is often used as an evaluation criterion.
It cannot be used as a training criterion though since the gradient is not
defined for it.
Example:
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
>>> # Note that non-1 values are treated as 0
>>> C.classification_error([[1., 2., 3., 4.]], [[5., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
Args:
output_vector: the output values from the network
target_vector: it is one-hot vector where the hot bit corresponds to
the label index.
axis (int or :class:`~cntk.axis.Axis`): axis along which the
classification error will be computed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import classification_error
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return classification_error(output_vector, target_vector, topN, axis, name)
def cross_entropy_with_softmax(output_vector, target_vector, axis=-1, name=''):
r'''
This operation computes the cross entropy between the ``target_vector`` and
the softmax of the ``output_vector``. The elements of ``target_vector``
have to be non-negative and should sum to 1. The ``output_vector`` can
contain any values. The function will internally compute the softmax of
the ``output_vector``. Concretely,
:math:`\mathrm{softmax}(x)=\left[\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\ldots\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\right]`
:math:`\mathrm{cross\_entropy\_with\_softmax}(o, t) = -\sum_{i} t_i \log(\mathrm{softmax}(o)_i)`
with the understanding that the implementation can use equivalent formulas
for efficiency and numerical stability.
Example:
>>> C.cross_entropy_with_softmax([[1., 1., 1., 50.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.cross_entropy_with_softmax([[1., 2., 3., 4.]], [[0.35, 0.15, 0.05, 0.45]]).eval()
array([[ 1.84019]], dtype=float32)
Args:
output_vector: the unscaled computed output values from the network
target_vector: usually it is one-hot vector where the hot bit
corresponds to the label index. But it can be any probability
distribution over the labels.
axis (int or :class:`~cntk.axis.Axis`, optional): if given, cross entropy will be computed
along this axis
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cross_entropy_with_softmax
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return cross_entropy_with_softmax(output_vector, target_vector, axis, name)
def cross_entropy_with_softmax(output_vector, target_vector, axis=-1, name=''):
r'''
This operation computes the cross entropy between the ``target_vector`` and
the softmax of the ``output_vector``. The elements of ``target_vector``
have to be non-negative and should sum to 1. The ``output_vector`` can
contain any values. The function will internally compute the softmax of
the ``output_vector``. Concretely,
:math:`\mathrm{softmax}(x)=\left[\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\ldots\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\right]`
:math:`\mathrm{cross\_entropy\_with\_softmax}(o, t) = -\sum_{i} t_i \log(\mathrm{softmax}(o)_i)`
with the understanding that the implementation can use equivalent formulas
for efficiency and numerical stability.
Example:
>>> C.cross_entropy_with_softmax([[1., 1., 1., 50.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.cross_entropy_with_softmax([[1., 2., 3., 4.]], [[0.35, 0.15, 0.05, 0.45]]).eval()
array([[ 1.84019]], dtype=float32)
Args:
output_vector: the unscaled computed output values from the network
target_vector: usually it is one-hot vector where the hot bit
corresponds to the label index. But it can be any probability
distribution over the labels.
axis (int or :class:`~cntk.axis.Axis`, optional): if given, cross entropy will be computed
along this axis
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cross_entropy_with_softmax
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return cross_entropy_with_softmax(output_vector, target_vector, axis, name)
def classification_error(output_vector, target_vector, axis=-1, topN=1, name=''):
'''
This operation computes the classification error. It finds the index of the highest
value in the output_vector and compares it to the actual ground truth label
(the index of the hot bit in the target vector). The result is a scalar
(i.e., one by one matrix). This is often used as an evaluation criterion.
It cannot be used as a training criterion though since the gradient is not
defined for it.
Example:
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
>>> # Note that non-1 values are treated as 0
>>> C.classification_error([[1., 2., 3., 4.]], [[5., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
Args:
output_vector: the output values from the network
target_vector: it is one-hot vector where the hot bit corresponds to
the label index.
axis (int or :class:`~cntk.axis.Axis`): axis along which the
classification error will be computed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import classification_error
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return classification_error(output_vector, target_vector, topN, axis, name)
