Metrics¶

Accuracy
AUC
CMC score
Dice
F1 score
Focal
Hitrate
IoU
MRR
MAP
NDCG
Precision
Recall
Functional

Accuracy ¶

Various accuracy metrics:

accuracy()
multi_label_accuracy()

catalyst.metrics.accuracy.accuracy(outputs: torch.Tensor, targets: torch.Tensor, topk: Sequence[int] = (1, ), activation: Optional[str] = None) → Sequence[torch.Tensor][source]¶

Computes multi-class accuracy@topk for the specified values of topk.

Parameters

outputs – model outputs, logits with shape [bs; num_classes]
targets – ground truth, labels with shape [bs; 1]
activation – activation to use for model output
topk – topk for accuracy@topk computing

Returns

list with computed accuracy@topk

catalyst.metrics.accuracy.multi_label_accuracy(outputs: torch.Tensor, targets: torch.Tensor, threshold: Union[float, torch.Tensor], activation: Optional[str] = None) → torch.Tensor[source]¶

Computes multi-label accuracy for the specified activation and threshold.

Parameters

outputs – NxK tensor that for each of the N examples indicates the probability of the example belonging to each of the K classes, according to the model.
targets – binary NxK tensort that encodes which of the K classes are associated with the N-th input (eg: a row [0, 1, 0, 1] indicates that the example is associated with classes 2 and 4)
threshold – threshold for for model output
activation – activation to use for model output

Returns

computed multi-label accuracy

AUC ¶

catalyst.metrics.auc.auc(outputs: torch.Tensor, targets: torch.Tensor) → torch.Tensor[source]¶

AUC metric.

Parameters

outputs – [bs; num_classes] estimated scores from a model.
targets – [bs; num_classes] ground truth (correct) target values.

Returns

Tensor with [num_classes] shape of per-class-aucs

Return type

torch.Tensor

CMC score ¶

catalyst.metrics.cmc_score.cmc_score_count(distances: torch.Tensor, conformity_matrix: torch.Tensor, topk: int = 1) → float[source]¶

Function to count CMC from distance matrix and conformity matrix.

Parameters

distances – distance matrix shape of (n_embeddings_x, n_embeddings_y)
conformity_matrix – binary matrix with 1 on same label pos and 0 otherwise
topk – number of top examples for cumulative score counting

Returns

cmc score

catalyst.metrics.cmc_score.cmc_score(query_embeddings: torch.Tensor, gallery_embeddings: torch.Tensor, conformity_matrix: torch.Tensor, topk: int = 1) → float[source]¶

Function to count CMC score from query and gallery embeddings.

Parameters

query_embeddings – tensor shape of (n_embeddings, embedding_dim) embeddings of the objects in querry
gallery_embeddings – tensor shape of (n_embeddings, embedding_dim) embeddings of the objects in gallery
conformity_matrix – binary matrix with 1 on same label pos and 0 otherwise
topk – number of top examples for cumulative score counting

Returns

cmc score

Dice ¶

Dice metric.

catalyst.metrics.dice.dice(outputs: torch.Tensor, targets: torch.Tensor, eps: float = 1e-07, threshold: float = None, activation: str = 'Sigmoid')[source]¶

Computes the dice metric.

Parameters

outputs – a list of predicted elements
targets – a list of elements that are to be predicted
eps – epsilon
threshold – threshold for outputs binarization
activation – An torch.nn activation applied to the outputs. Must be one of [“none”, “Sigmoid”, “Softmax2d”]

Returns

Dice score

Return type

float

catalyst.metrics.dice.calculate_dice(true_positives: numpy.array, false_positives: numpy.array, false_negatives: numpy.array) → numpy.array[source]¶

Calculate list of Dice coefficients.

Parameters

true_positives – true positives numpy tensor
false_positives – false positives numpy tensor
false_negatives – false negatives numpy tensor

Returns

dice score

Return type

np.array

Raises

ValueError – if dice is out of [0; 1] bounds

catalyst.metrics.f1_score.f1_score(outputs: torch.Tensor, targets: torch.Tensor, eps: float = 1e-07, argmax_dim: int = -1, num_classes: Optional[int] = None) → Union[float, torch.Tensor][source]¶

Fbeta_score with beta=1.

Parameters

outputs – A list of predicted elements
targets – A list of elements that are to be predicted
eps – epsilon to avoid zero division
argmax_dim – int, that specifies dimension for argmax transformation in case of scores/probabilities in outputs
num_classes – int, that specifies number of classes if it known

Returns

F_1 score

Return type

float

catalyst.metrics.f1_score.fbeta_score(outputs: torch.Tensor, targets: torch.Tensor, beta: float = 1.0, eps: float = 1e-07, argmax_dim: int = -1, num_classes: Optional[int] = None) → Union[float, torch.Tensor][source]¶

Counts fbeta score for given outputs and targets.

Parameters

outputs – A list of predicted elements
targets – A list of elements that are to be predicted
beta – beta param for f_score
eps – epsilon to avoid zero division
argmax_dim – int, that specifies dimension for argmax transformation in case of scores/probabilities in outputs
num_classes – int, that specifies number of classes if it known

Raises

Exception – If beta is a negative number.

Returns

F_1 score.

Return type

float

Focal ¶

Focal losses:

sigmoid_focal_loss()
reduced_focal_loss()

catalyst.metrics.focal.sigmoid_focal_loss(outputs: torch.Tensor, targets: torch.Tensor, gamma: float = 2.0, alpha: float = 0.25, reduction: str = 'mean')[source]¶

Compute binary focal loss between target and output logits.

Parameters

outputs – tensor of arbitrary shape
targets – tensor of the same shape as input
gamma – gamma for focal loss
alpha – alpha for focal loss
reduction (string, optional) – specifies the reduction to apply to the output: "none" | "mean" | "sum" | "batchwise_mean". "none": no reduction will be applied, "mean": the sum of the output will be divided by the number of elements in the output, "sum": the output will be summed.

Returns

computed loss

Source: https://github.com/BloodAxe/pytorch-toolbelt

catalyst.metrics.focal.reduced_focal_loss(outputs: torch.Tensor, targets: torch.Tensor, threshold: float = 0.5, gamma: float = 2.0, reduction='mean') → torch.Tensor[source]¶

Compute reduced focal loss between target and output logits.

It has been proposed in Reduced Focal Loss: 1st Place Solution to xView object detection in Satellite Imagery paper.

Note

size_average and reduce params are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction.

Source: https://github.com/BloodAxe/pytorch-toolbelt

Parameters

outputs – tensor of arbitrary shape
targets – tensor of the same shape as input
threshold – threshold for focal reduction
gamma – gamma for focal reduction
reduction (string, optional) – specifies the reduction to apply to the output: "none" | "mean" | "sum" | "batchwise_mean". "none": no reduction will be applied, "mean": the sum of the output will be divided by the number of elements in the output, "sum": the output will be summed. "batchwise_mean" computes mean loss per sample in batch. Default: “mean”

Returns: # noqa: DAR201: torch.Tensor: computed loss

Hitrate ¶

Hitrate metric:

hitrate()

catalyst.metrics.hitrate.hitrate(outputs: torch.Tensor, targets: torch.Tensor, k=10) → torch.Tensor[source]¶

Calculate the hit rate score given model outputs and targets. Hit-rate is a metric for evaluating ranking systems. Generate top-N recommendations and if one of the recommendation is actually what user has rated, you consider that a hit. By rate we mean any explicit form of user’s interactions. Add up all of the hits for all users and then divide by number of users

Compute top-N recomendation for each user in the training stage and intentionally remove one of this items fro the training data.

Parameters

outputs (torch.Tensor) – Tensor weith predicted score size: [batch_size, slate_length] model outputs, logits
targets (torch.Tensor) – Binary tensor with ground truth. 1 means the item is relevant for the user and 0 not relevant size: [batch_szie, slate_length] ground truth, labels
k (int) – Parameter fro evaluation on top-k items

Returns

the hit rate score

Return type

hitrate (torch.Tensor)

IoU ¶

IoU metric. Jaccard metric refers to IoU here, same functionality.

catalyst.metrics.iou.iou(outputs: torch.Tensor, targets: torch.Tensor, classes: List[str] = None, eps: float = 1e-07, threshold: float = None, activation: str = 'Sigmoid') → torch.Tensor[source]¶

Parameters

outputs – A list of predicted elements
targets – A list of elements that are to be predicted
classes – if classes are specified we reduce across all dims except channels
eps – epsilon to avoid zero division
threshold – threshold for outputs binarization
activation – An torch.nn activation applied to the outputs. Must be one of [“none”, “Sigmoid”, “Softmax2d”]

Returns

IoU (Jaccard) score(s)

Return type

Union[float, List[float]]

catalyst.metrics.iou.jaccard(outputs: torch.Tensor, targets: torch.Tensor, classes: List[str] = None, eps: float = 1e-07, threshold: float = None, activation: str = 'Sigmoid') → torch.Tensor¶

Parameters

outputs – A list of predicted elements
targets – A list of elements that are to be predicted
classes – if classes are specified we reduce across all dims except channels
eps – epsilon to avoid zero division
threshold – threshold for outputs binarization
activation – An torch.nn activation applied to the outputs. Must be one of [“none”, “Sigmoid”, “Softmax2d”]

Returns

IoU (Jaccard) score(s)

Return type

Union[float, List[float]]

MRR ¶

MRR metric.

catalyst.metrics.mrr.mrr(outputs: torch.Tensor, targets: torch.Tensor, k=100) → torch.Tensor[source]¶

Calculate the Mean Reciprocal Rank (MRR) score given model ouptputs and targets User’s data aggreagtesd in batches.

The MRR@k is the mean overall user of the reciprocal rank, that is the rank of the highest ranked relevant item, if any in the top k, 0 otherwise. https://en.wikipedia.org/wiki/Mean_reciprocal_rank

Parameters

outputs (torch.Tensor) – Tensor weith predicted score size: [batch_size, slate_length] model outputs, logits
targets (torch.Tensor) – Binary tensor with ground truth. 1 means the item is relevant for the user and 0 not relevant size: [batch_szie, slate_length] ground truth, labels
k (int) – Parameter fro evaluation on top-k items

Returns

The mrr score for each user.

Return type

result (torch.Tensor)

MAP ¶

MAP metric.

catalyst.metrics.avg_precision.mean_avg_precision(outputs: torch.Tensor, targets: torch.Tensor, top_k: List[int]) → Dict[str, int][source]¶

Calculate the mean average precision (MAP) for RecSys. The metrics calculate the mean of the AP across all batches

MAP amplifies the interest in finding many relevant items for each query

Parameters

outputs (torch.Tensor) – Tensor weith predicted score size: [batch_size, slate_length] model outputs, logits
targets (torch.Tensor) – Binary tensor with ground truth. 1 means the item is relevant and 0 not relevant size: [batch_szie, slate_length] ground truth, labels
top_k (List[int]) – List of parameter for evaluation topK items

Returns

The map score for every k. size: [len(top_k), 1]

Return type

result (Dict[str, int])

catalyst.metrics.avg_precision.avg_precision(outputs: torch.Tensor, targets: torch.Tensor, k=10) → torch.Tensor[source]¶

Calculate the Average Precision for RecSys. The precision metric summarizes the fraction of relevant items out of the whole the recommendation list.

To compute the precision at k set the threshold rank k, compute the percentage of relevant items in topK, ignoring the documents ranked lower than k.

The average precision at k (AP at k) summarizes the average precision for relevant items up to the k-th one. Wikipedia entry for the Average precision

<https://en.wikipedia.org/w/index.php?title=Information_retrieval& oldid=793358396#Average_precision>

If a relevant document never gets retrieved, we assume the precision corresponding to that relevant doc to be zero

Parameters

outputs (torch.Tensor) – Tensor weith predicted score size: [batch_size, slate_length] model outputs, logits
targets (torch.Tensor) – Binary tensor with ground truth. 1 means the item is relevant and 0 not relevant size: [batch_szie, slate_length] ground truth, labels
k (int) – The position to compute the truncated AP, must be positive

Returns

The map score for each batch. size: [batch_size, 1]

Return type

result (torch.Tensor)

NDCG ¶

Discounted Cumulative Gain metrics

catalyst.metrics.ndcg.dcg(outputs: torch.Tensor, targets: torch.Tensor, k=10, gain_function='pow_rank') → torch.Tensor[source]¶

Computes DCG@topk for the specified values of k. Graded relevance as a measure of usefulness, or gain, from examining a set of items. Gain may be reduced at lower ranks. Reference: https://en.wikipedia.org/wiki/Discounted_cumulative_gain

Parameters

outputs (torch.Tensor) – model outputs, logits with shape [batch_size; slate_length]
targets (torch.Tensor) – ground truth, labels with shape [batch_size; slate_length]
gain_function – String indicates the gain function for the ground truth labels. Two options available: - pow_rank: torch.pow(2, x) - 1 - rank: x On the default, pow_rank is used to emphasize on retrievng the relevant documents.
k (int) – Parameter fro evaluation on top-k items

Returns

torch.Tensor for dcg at k

Raises

ValueError – gain function can be either pow_rank or rank

catalyst.metrics.ndcg.ndcg(outputs: torch.Tensor, targets: torch.Tensor, top_k: List[int], gain_function='pow_rank') → torch.Tensor[source]¶

Computes nDCG@topk for the specified values of top_k.

Parameters

outputs (torch.Tensor) – model outputs, logits with shape [batch_size; slate_size]
targets (torch.Tensor) – ground truth, labels with shape [batch_size; slate_size]
gain_function – callable, gain function for the ground truth labels. on the deafult, the torch.pow(2, x) - 1 function used to get emphasise on the retirvng the revelant documnets.
top_k (List[int]) – Parameter fro evaluation on top-k items

Returns

tuple with computed ndcg@topk

Precision ¶

catalyst.metrics.precision.average_precision(outputs: torch.Tensor, targets: torch.Tensor, weights: Optional[torch.Tensor] = None) → torch.Tensor[source]¶

Computes the average precision.

Parameters

outputs – NxK tensor that for each of the N examples indicates the probability of the example belonging to each of the K classes, according to the model.
targets – binary NxK tensort that encodes which of the K classes are associated with the N-th input (eg: a row [0, 1, 0, 1] indicates that the example is associated with classes 2 and 4)
weights – importance for each sample

Returns

tensor of [K; ] shape, with average precision for K classes

Return type

torch.Tensor

catalyst.metrics.precision.precision(outputs: torch.Tensor, targets: torch.Tensor, argmax_dim: int = -1, eps: float = 1e-07, num_classes: Optional[int] = None) → Union[float, torch.Tensor][source]¶

Multiclass precision metric.

Parameters

outputs – estimated targets as predicted by a model with shape [bs; …, (num_classes or 1)]
targets – ground truth (correct) target values with shape [bs; …, 1]
argmax_dim – int, that specifies dimension for argmax transformation in case of scores/probabilities in outputs
eps – float. Epsilon to avoid zero division.
num_classes – int, that specifies number of classes if it known

Returns

Return type

Tensor

Recall ¶

catalyst.metrics.recall.recall(outputs: torch.Tensor, targets: torch.Tensor, argmax_dim: int = -1, eps: float = 1e-07, num_classes: Optional[int] = None) → Union[float, torch.Tensor][source]¶

Multiclass precision metric.

Parameters

outputs – estimated targets as predicted by a model with shape [bs; …, (num_classes or 1)]
targets – ground truth (correct) target values with shape [bs; …, 1]
argmax_dim – int, that specifies dimension for argmax transformation in case of scores/probabilities in outputs
eps – float. Epsilon to avoid zero division.
num_classes – int, that specifies number of classes if it known.

Returns

recall for every class

Return type

Tensor

Functional ¶

catalyst.metrics.functional.process_multilabel_components(outputs: torch.Tensor, targets: torch.Tensor, weights: Optional[torch.Tensor] = None) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor][source]¶

General preprocessing for multi-label-based metrics.

Parameters

outputs – NxK tensor that for each of the N examples indicates the probability of the example belonging to each of the K classes, according to the model.
targets – binary NxK tensor that encodes which of the K classes are associated with the N-th input (eg: a row [0, 1, 0, 1] indicates that the example is associated with classes 2 and 4)
weights – importance for each sample

Returns

processed outputs and targets with [batch_size; num_classes] shape

catalyst.metrics.functional.get_binary_statistics(outputs: torch.Tensor, targets: torch.Tensor, label: int = 1) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor][source]¶

Computes the number of true negative, false positive, false negative, true negative and support for a binary classification problem for a given label.

Parameters

outputs – estimated targets as predicted by a model with shape [bs; …, 1]
targets – ground truth (correct) target values with shape [bs; …, 1]
label – integer, that specifies label of interest for statistics compute

Returns

stats

Return type

Tuple[Tensor, Tensor, Tensor, Tensor, Tensor]

Example

>>> y_pred = torch.tensor([[0, 0, 1, 1, 0, 1, 0, 1]])
>>> y_true = torch.tensor([[0, 1, 0, 1, 0, 0, 1, 1]])
>>> tn, fp, fn, tp, support = get_binary_statistics(y_pred, y_true)
tensor(2) tensor(2) tensor(2) tensor(2) tensor(4)

catalyst.metrics.functional.get_multiclass_statistics(outputs: torch.Tensor, targets: torch.Tensor, argmax_dim: int = -1, num_classes: Optional[int] = None) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor][source]¶

Computes the number of true negative, false positive, false negative, true negative and support for a multi-class classification problem.

Parameters

outputs – estimated targets as predicted by a model with shape [bs; …, (num_classes or 1)]
targets – ground truth (correct) target values with shape [bs; …, 1]
argmax_dim – int, that specifies dimension for argmax transformation in case of scores/probabilities in outputs
num_classes – int, that specifies number of classes if it known

Returns

stats

Return type

Tuple[Tensor, Tensor, Tensor, Tensor, Tensor]

Example

>>> y_pred = torch.tensor([1, 2, 3, 0])
>>> y_true = torch.tensor([1, 3, 4, 0])
>>> tn, fp, fn, tp, support = get_multiclass_statistics(y_pred, y_true)
tensor([3., 3., 3., 2., 3.]), tensor([0., 0., 1., 1., 0.]),
tensor([0., 0., 0., 1., 1.]), tensor([1., 1., 0., 0., 0.]),
tensor([1., 1., 0., 1., 1.])

catalyst.metrics.functional.get_multilabel_statistics(outputs: torch.Tensor, targets: torch.Tensor) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor][source]¶

Computes the number of true negative, false positive, false negative, true negative and support for a multi-label classification problem.

Parameters

outputs – estimated targets as predicted by a model with shape [bs; …, (num_classes or 1)]
targets – ground truth (correct) target values with shape [bs; …, 1]

Returns

stats

Return type

Tuple[Tensor, Tensor, Tensor, Tensor, Tensor]

Example

>>> y_pred = torch.tensor([[0, 0, 1, 1], [0, 1, 0, 1]])
>>> y_true = torch.tensor([[0, 1, 0, 1], [0, 0, 1, 1]])
>>> tn, fp, fn, tp, support = get_multilabel_statistics(y_pred, y_true)
tensor([2., 0., 0., 0.]) tensor([0., 1., 1., 0.]),
tensor([0., 1., 1., 0.]) tensor([0., 0., 0., 2.]),
tensor([0., 1., 1., 2.])

>>> y_pred = torch.tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> y_true = torch.tensor([0, 1, 2])
>>> tn, fp, fn, tp, support = get_multilabel_statistics(y_pred, y_true)
tensor([2., 2., 2.]) tensor([0., 0., 0.])
tensor([0., 0., 0.]) tensor([1., 1., 1.])
tensor([1., 1., 1.])

>>> y_pred = torch.tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> y_true = torch.nn.functional.one_hot(torch.tensor([0, 1, 2]))
>>> tn, fp, fn, tp, support = get_multilabel_statistics(y_pred, y_true)
tensor([2., 2., 2.]) tensor([0., 0., 0.])
tensor([0., 0., 0.]) tensor([1., 1., 1.])
tensor([1., 1., 1.])

catalyst.metrics.functional.get_default_topk_args(num_classes: int) → Sequence[int][source]¶

Calculate list params for Accuracy@k and mAP@k.

Parameters: num_classes – number of classes
Returns: array of accuracy arguments
Return type: iterable

Examples

>>> get_default_topk_args(num_classes=4)
[1, 3]

>>> get_default_topk_args(num_classes=8)
[1, 3, 5]

catalyst.metrics.functional.wrap_topk_metric2dict(metric_fn: Callable, topk_args: Sequence[int]) → Callable[source]¶

Logging wrapper for metrics with Sequence[Union[torch.Tensor, int, float, Dict]] output. Computes the metric and sync each element from the output sequence with passed topk argument.

Parameters

metric_fn – metric function to compute
topk_args – topk args to sync outputs with

Returns

wrapped metric function with List[Dict] output

Raises

NotImplementedError – if metrics returned values are out of torch.Tensor, int, float, Dict union.

catalyst.metrics.functional.wrap_class_metric2dict(metric_fn: Callable, class_args: Sequence[str] = None) → Callable[source]¶

# noqa: D202 Logging wrapper for metrics with torch.Tensor output and [num_classes] shape. Computes the metric and sync each element from the output Tensor with passed class argument.

Parameters

metric_fn – metric function to compute
class_args – class names for logging. default: None - class indexes will be used.

Returns

wrapped metric function with List[Dict] output