# Approximates the AUC (Area under the curve) of the ROC or PR curves.

Source:`R/metrics.R`

`metric_auc.Rd`

The AUC (Area under the curve) of the ROC (Receiver operating characteristic; default) or PR (Precision Recall) curves are quality measures of binary classifiers. Unlike the accuracy, and like cross-entropy losses, ROC-AUC and PR-AUC evaluate all the operational points of a model.

This class approximates AUCs using a Riemann sum. During the metric accumulation phrase, predictions are accumulated within predefined buckets by value. The AUC is then computed by interpolating per-bucket averages. These buckets define the evaluated operational points.

This metric creates four local variables, `true_positives`

,
`true_negatives`

, `false_positives`

and `false_negatives`

that are used to
compute the AUC. To discretize the AUC curve, a linearly spaced set of
thresholds is used to compute pairs of recall and precision values. The area
under the ROC-curve is therefore computed using the height of the recall
values by the false positive rate, while the area under the PR-curve is the
computed using the height of the precision values by the recall.

This value is ultimately returned as `auc`

, an idempotent operation that
computes the area under a discretized curve of precision versus recall
values (computed using the aforementioned variables). The `num_thresholds`

variable controls the degree of discretization with larger numbers of
thresholds more closely approximating the true AUC. The quality of the
approximation may vary dramatically depending on `num_thresholds`

. The
`thresholds`

parameter can be used to manually specify thresholds which
split the predictions more evenly.

For a best approximation of the real AUC, `predictions`

should be
distributed approximately uniformly in the range `[0, 1]`

(if
`from_logits=FALSE`

). The quality of the AUC approximation may be poor if
this is not the case. Setting `summation_method`

to 'minoring' or 'majoring'
can help quantify the error in the approximation by providing lower or upper
bound estimate of the AUC.

If `sample_weight`

is `NULL`

, weights default to 1.
Use `sample_weight`

of 0 to mask values.

## Usage

```
metric_auc(
...,
num_thresholds = 200L,
curve = "ROC",
summation_method = "interpolation",
name = NULL,
dtype = NULL,
thresholds = NULL,
multi_label = FALSE,
num_labels = NULL,
label_weights = NULL,
from_logits = FALSE
)
```

## Arguments

- ...
For forward/backward compatability.

- num_thresholds
(Optional) The number of thresholds to use when discretizing the roc curve. Values must be > 1. Defaults to

`200`

.- curve
(Optional) Specifies the name of the curve to be computed,

`'ROC'`

(default) or`'PR'`

for the Precision-Recall-curve.- summation_method
(Optional) Specifies the Riemann summation method used. 'interpolation' (default) applies mid-point summation scheme for

`ROC`

. For PR-AUC, interpolates (true/false) positives but not the ratio that is precision (see Davis & Goadrich 2006 for details); 'minoring' applies left summation for increasing intervals and right summation for decreasing intervals; 'majoring' does the opposite.- name
(Optional) string name of the metric instance.

- dtype
(Optional) data type of the metric result.

- thresholds
(Optional) A list of floating point values to use as the thresholds for discretizing the curve. If set, the

`num_thresholds`

parameter is ignored. Values should be in`[0, 1]`

. Endpoint thresholds equal to {`-epsilon`

,`1+epsilon`

} for a small positive epsilon value will be automatically included with these to correctly handle predictions equal to exactly 0 or 1.- multi_label
boolean indicating whether multilabel data should be treated as such, wherein AUC is computed separately for each label and then averaged across labels, or (when

`FALSE`

) if the data should be flattened into a single label before AUC computation. In the latter case, when multilabel data is passed to AUC, each label-prediction pair is treated as an individual data point. Should be set to FALSE for multi-class data.- num_labels
(Optional) The number of labels, used when

`multi_label`

is TRUE. If`num_labels`

is not specified, then state variables get created on the first call to`update_state`

.- label_weights
(Optional) list, array, or tensor of non-negative weights used to compute AUCs for multilabel data. When

`multi_label`

is TRUE, the weights are applied to the individual label AUCs when they are averaged to produce the multi-label AUC. When it's FALSE, they are used to weight the individual label predictions in computing the confusion matrix on the flattened data. Note that this is unlike`class_weights`

in that`class_weights`

weights the example depending on the value of its label, whereas`label_weights`

depends only on the index of that label before flattening; therefore`label_weights`

should not be used for multi-class data.- from_logits
boolean indicating whether the predictions (

`y_pred`

in`update_state`

) are probabilities or sigmoid logits. As a rule of thumb, when using a keras loss, the`from_logits`

constructor argument of the loss should match the AUC`from_logits`

constructor argument.

## Value

a `Metric`

instance is returned. The `Metric`

instance can be passed
directly to `compile(metrics = )`

, or used as a standalone object. See
`?Metric`

for example usage.

## Usage

Standalone usage:

```
m <- metric_auc(num_thresholds = 3)
m$update_state(c(0, 0, 1, 1),
c(0, 0.5, 0.3, 0.9))
# threshold values are [0 - 1e-7, 0.5, 1 + 1e-7]
# tp = [2, 1, 0], fp = [2, 0, 0], fn = [0, 1, 2], tn = [0, 2, 2]
# tp_rate = recall = [1, 0.5, 0], fp_rate = [1, 0, 0]
# auc = ((((1 + 0.5) / 2) * (1 - 0)) + (((0.5 + 0) / 2) * (0 - 0)))
# = 0.75
m$result()
```

```
m$reset_state()
m$update_state(c(0, 0, 1, 1),
c(0, 0.5, 0.3, 0.9),
sample_weight=c(1, 0, 0, 1))
m$result()
```

Usage with `compile()`

API:

```
# Reports the AUC of a model outputting a probability.
model |> compile(
optimizer = 'sgd',
loss = loss_binary_crossentropy(),
metrics = list(metric_auc())
)
# Reports the AUC of a model outputting a logit.
model |> compile(
optimizer = 'sgd',
loss = loss_binary_crossentropy(from_logits = TRUE),
metrics = list(metric_auc(from_logits = TRUE))
)
```

## See also

Other confusion metrics: `metric_false_negatives()`

`metric_false_positives()`

`metric_precision()`

`metric_precision_at_recall()`

`metric_recall()`

`metric_recall_at_precision()`

`metric_sensitivity_at_specificity()`

`metric_specificity_at_sensitivity()`

`metric_true_negatives()`

`metric_true_positives()`

Other metrics: `Metric()`

`custom_metric()`

`metric_binary_accuracy()`

`metric_binary_crossentropy()`

`metric_binary_focal_crossentropy()`

`metric_binary_iou()`

`metric_categorical_accuracy()`

`metric_categorical_crossentropy()`

`metric_categorical_focal_crossentropy()`

`metric_categorical_hinge()`

`metric_cosine_similarity()`

`metric_f1_score()`

`metric_false_negatives()`

`metric_false_positives()`

`metric_fbeta_score()`

`metric_hinge()`

`metric_huber()`

`metric_iou()`

`metric_kl_divergence()`

`metric_log_cosh()`

`metric_log_cosh_error()`

`metric_mean()`

`metric_mean_absolute_error()`

`metric_mean_absolute_percentage_error()`

`metric_mean_iou()`

`metric_mean_squared_error()`

`metric_mean_squared_logarithmic_error()`

`metric_mean_wrapper()`

`metric_one_hot_iou()`

`metric_one_hot_mean_iou()`

`metric_poisson()`

`metric_precision()`

`metric_precision_at_recall()`

`metric_r2_score()`

`metric_recall()`

`metric_recall_at_precision()`

`metric_root_mean_squared_error()`

`metric_sensitivity_at_specificity()`

`metric_sparse_categorical_accuracy()`

`metric_sparse_categorical_crossentropy()`

`metric_sparse_top_k_categorical_accuracy()`

`metric_specificity_at_sensitivity()`

`metric_squared_hinge()`

`metric_sum()`

`metric_top_k_categorical_accuracy()`

`metric_true_negatives()`

`metric_true_positives()`