cntk.metrics package¶

Evaluation metrics.

classification_error(output_vector, target_vector, axis=-1, topN=1, name='')[source]

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)

Parameters: 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 Axis) – axis along which the classification error will be computed. name (str, optional) – the name of the Function instance in the network Function
edit_distance_error(input_a, input_b, subPen=1, delPen=1, insPen=1, squashInputs=False, tokensToIgnore=[], name='')[source]

Edit distance error evaluation function with the option of specifying penalty of substitution, deletion and insertion, as well as squashing the input sequences and ignoring certain samples. Using the classic DP algorithm as described in https://en.wikipedia.org/wiki/Edit_distance, adjusted to take into account the penalties.

Each sequence in the inputs is expected to be a matrix. Prior to computation of the edit distance, the operation extracts the indices of maximum element in each column. For example, a sequence matrix

1 2 9 1

3 0 3 2

will be represented as the vector of labels (indices) as [1, 0, 0, 1], on which edit distance will be actually evaluated.

The function allows to squash sequences of repeating labels and ignore certain labels. For example, if squashInputs is true and tokensToIgnore contains index of label ‘-‘ then given first input sequence as s1=”1-12-” and second as s2=”-11–122” the edit distance will be computed against s1’ = “112” and s2’ = “112”.

When used as an evaluation criterion, the Trainer will aggregate all values over an epoch and report the average, i.e. the error rate. Primary objective of this node is for error evaluation of CTC training, see formula (1) in “Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks”, ftp://ftp.idsia.ch/pub/juergen/icml2006.pdf

Example

>>> i1 = C.input(shape=(2,))
>>> i2 = C.input(shape=(2,))
>>> arguments = {i1 : [[1, 3], [2, 0]], i2 : [[2, 0], [2, 0]]}
>>> a = C.edit_distance_error(i1, i2, 0, 1, 1, True, [1])
>>> a.eval(arguments)
array(1.0, dtype=float32)

Parameters: input_a – first input sequence input_b – second input sequence subPen – substitution penalty delPen – deletion penalty insPen – insertion penalty squashInputs – whether to merge sequences of identical samples (in both input sequences). If true and tokensToIgnore contains label ‘-‘ then given first input sequence as s1=”a-ab-” and second as s2=”-aa–abb” the edit distance will be computed against s1’ = “aab” and s2’ = “aab”. tokensToIgnore – list of indices of samples to ignore during edit distance evaluation (in both sequences) name (str, optional) – the name of the Function instance in the network Function
ndcg_at_1(output, gain, group, name='')[source]

Groups samples according to group, sorts them within each group based on output and computes the Normalized Discounted Cumulative Gain (NDCG) at 1 for each group. Concretely, the NDCG at 1 is:

$$\mathrm{NDCG_1} = \frac{gain_{(1)}}{\max_i gain_i}$$

where $$gain_{(1)}$$ means the gain of the first ranked sample.

Samples in the same group must appear in order of decreasing gain.

It returns the average NDCG at 1 across all the groups in the minibatch multiplied by 100 times the number of samples in the minibatch.

This is a forward-only operation, there is no gradient for it.

Example

>>> group = C.input_variable((1,))
>>> score = C.input_variable((1,))
>>> gain  = C.input_variable((1,))
>>> g = np.array([1, 1, 2, 2], dtype=np.float32).reshape(4,1,1)
>>> s = np.array([2, 1, 3, 1], dtype=np.float32).reshape(4,1,1)
>>> n = np.array([7, 1, 3, 1], dtype=np.float32).reshape(4,1,1)
>>> C.ndcg_at_1(score, gain, group).eval({score:s, gain:n, group: g})
array(400.0, dtype=float32)

Parameters: 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 Function