def lambda_rank(output, gain, group, name=''):
r'''
Groups samples according to ``group``, sorts
them within each group based on ``output`` and
computes the Normalized Discounted Cumulative Gain
(NDCG) at infinity for each group. Concretely,
the Discounted Cumulative Gain (DCG) at infinity is:
:math:`\mathrm{DCG_{\infty}}()=\sum_{i=0}^{\infty} \frac{gain_{(i)}}{\log(i+2)}`
where :math:`gain_{(i)}` means the gain of the :math:`i`-th ranked sample.
The NDCG is just the DCG divided by the maximum achievable DCG (obtained
by placing the samples with the largest gain at the top of the ranking).
Samples in the same group must appear in order of decreasing gain.
It returns 1 minus the average NDCG across all the groups in the minibatch
multiplied by 100 times the number of samples in the minibatch.
In the backward direction it back-propagates LambdaRank gradients.
Example:
>>> group = C.input_variable((1,))
>>> score = C.input_variable((1,), needs_gradient=True)
>>> gain = C.input_variable((1,))
>>> g = np.array([1, 1, 2, 2], dtype=np.float32).reshape(4,1,1)
>>> s = np.array([1, 2, 3, 4], dtype=np.float32).reshape(4,1,1)
>>> n = np.array([7, 1, 3, 1], dtype=np.float32).reshape(4,1,1)
>>> f = C.lambda_rank(score, gain, group)
>>> np.round(f.grad({score:s, gain:n, group: g}, wrt=[score]),4)
array([[[-0.2121]],
<BLANKLINE>
[[ 0.2121]],
<BLANKLINE>
[[-0.1486]],
<BLANKLINE>
[[ 0.1486]]], dtype=float32)
Args:
output: score of each sample
gain: gain of each sample
group: group of each sample
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import lambda_rank
dtype = get_data_type(output, gain, group)
output = sanitize_input(output, dtype)
gain = sanitize_input(gain, dtype)
group = sanitize_input(group, dtype)
return lambda_rank(output, gain, group, name)
def lambda_rank(output, gain, group, name=''):
r'''
Groups samples according to ``group``, sorts
them within each group based on ``output`` and
computes the Normalized Discounted Cumulative Gain
(NDCG) at infinity for each group. Concretely,
the Discounted Cumulative Gain (DCG) at infinity is:
:math:`\mathrm{DCG_{\infty}}()=\sum_{i=0}^{\infty} \frac{gain_{(i)}}{\log(i+2)}`
where :math:`gain_{(i)}` means the gain of the :math:`i`-th ranked sample.
The NDCG is just the DCG divided by the maximum achievable DCG (obtained
by placing the samples with the largest gain at the top of the ranking).
Samples in the same group must appear in order of decreasing gain.
It returns 1 minus the average NDCG across all the groups in the minibatch
multiplied by 100 times the number of samples in the minibatch.
In the backward direction it back-propagates LambdaRank gradients.
Example:
>>> group = C.input_variable((1,))
>>> score = C.input_variable((1,), needs_gradient=True)
>>> gain = C.input_variable((1,))
>>> g = np.array([1, 1, 2, 2], dtype=np.float32).reshape(4,1)
>>> s = np.array([1, 2, 3, 4], dtype=np.float32).reshape(4,1)
>>> n = np.array([7, 1, 3, 1], dtype=np.float32).reshape(4,1)
>>> f = C.lambda_rank(score, gain, group)
>>> np.round(f.grad({score:s, gain:n, group: g}, wrt=[score]),4)
array([[-0.2121],
<BLANKLINE>
[ 0.2121],
<BLANKLINE>
[-0.1486],
<BLANKLINE>
[ 0.1486]], dtype=float32)
Args:
output: score of each sample
gain: gain of each sample
group: group of each sample
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import lambda_rank
dtype = get_data_type(output, gain, group)
output = sanitize_input(output, dtype)
gain = sanitize_input(gain, dtype)
group = sanitize_input(group, dtype)
return lambda_rank(output, gain, group, name)