Useful metrics for training

## Training metrics¶

Metrics for training fastai models are simply functions that take input and target tensors, and return some metric of interest for training. You can write your own metrics by defining a function of that type, and passing it to Learner in the metrics parameter, or use one of the following pre-defined functions.

## Predefined metrics:¶

#### accuracy[source][test]

accuracy(input:Tensor, targs:Tensor) → Rank0Tensor

Tests found for accuracy:

• pytest -sv tests/test_metrics.py::test_accuracy [source]
• pytest -sv tests/test_vision_train.py::test_accuracy [source]

To run tests please refer to this guide.

Computes accuracy with targs when input is bs * n_classes.

preds = tensor([0.4, 0.6], [0.3, 0.7], [0.2, 0.8], [0.6, 0.4], [0.9, 0.1]) # bs = 5, n = 2
ys = tensor([1], [0], [1], [0], [1])
accuracy(preds, ys)

tensor(0.6000)

#### accuracy_thresh[source][test]

accuracy_thresh(y_pred:Tensor, y_true:Tensor, thresh:float=0.5, sigmoid:bool=True) → Rank0Tensor

Tests found for accuracy_thresh:

• pytest -sv tests/test_metrics.py::test_accuracy_thresh [source]

To run tests please refer to this guide.

Computes accuracy when y_pred and y_true are the same size.

Predictions are compared to thresh after sigmoid is maybe applied. Then we count the numbers that match the targets.

preds = tensor([0.4, 0.6], [0.3, 0.7], [0.2, 0.8], [0.6, 0.4], [0.9, 0.1])
ys = tensor([0, 1], [1, 0], [0, 1], [1, 0], [0, 1])
accuracy_thresh(preds, ys, thresh=0.65, sigmoid=False)

tensor(0.4000)

#### top_k_accuracy[source][test]

top_k_accuracy(input:Tensor, targs:Tensor, k:int=5) → Rank0Tensor

Tests found for top_k_accuracy:

• pytest -sv tests/test_metrics.py::test_top_k_accuracy [source]

To run tests please refer to this guide.

Computes the Top-k accuracy (target is in the top k predictions).

#### dice[source][test]

dice(input:Tensor, targs:Tensor, iou:bool=False, eps:float=1e-08) → Rank0Tensor

Tests found for dice:

• pytest -sv tests/test_metrics.py::test_dice [source]
• pytest -sv tests/test_metrics.py::test_dice_iou [source]

To run tests please refer to this guide.

Dice coefficient metric for binary target. If iou=True, returns iou metric, classic for segmentation problems.

$$dice = \frac{2(TP)}{2(TP) + FP + FN}$$

where TP, FP and FN are the number of true positives, false positives and false negatives.

preds = tensor([0.4, 0.6], [0.3, 0.7], [0.2, 0.8], [0.6, 0.4], [0.9, 0.1])
ys = tensor([1], [0], [1], [0], [1])
dice(preds, ys) # TP = 2, FP = 1, FN = 1

tensor(0.6667)

#### error_rate[source][test]

error_rate(input:Tensor, targs:Tensor) → Rank0Tensor

Tests found for error_rate:

• pytest -sv tests/test_metrics.py::test_error_rate [source]
• pytest -sv tests/test_vision_train.py::test_error_rate [source]

To run tests please refer to this guide.

#### mean_squared_error[source][test]

mean_squared_error(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for mean_squared_error:

• pytest -sv tests/test_metrics.py::test_mse [source]

To run tests please refer to this guide.

Mean squared error between pred and targ.

#### mean_absolute_error[source][test]

mean_absolute_error(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for mean_absolute_error:

• pytest -sv tests/test_metrics.py::test_mae [source]

To run tests please refer to this guide.

Mean absolute error between pred and targ.

#### mean_squared_logarithmic_error[source][test]

mean_squared_logarithmic_error(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for mean_squared_logarithmic_error:

• pytest -sv tests/test_metrics.py::test_msle [source]

To run tests please refer to this guide.

Mean squared logarithmic error between pred and targ.

#### exp_rmspe[source][test]

exp_rmspe(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for exp_rmspe:

• pytest -sv tests/test_metrics.py::test_exp_rmspe [source]
• pytest -sv tests/test_metrics.py::test_exp_rmspe_num_of_ele [source]

To run tests please refer to this guide.

Exp RMSE between pred and targ.

#### root_mean_squared_error[source][test]

root_mean_squared_error(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for root_mean_squared_error:

• pytest -sv tests/test_metrics.py::test_rmse [source]

To run tests please refer to this guide.

Root mean squared error between pred and targ.

#### fbeta[source][test]

fbeta(y_pred:Tensor, y_true:Tensor, thresh:float=0.2, beta:float=2, eps:float=1e-09, sigmoid:bool=True) → Rank0Tensor

Tests found for fbeta:

• pytest -sv tests/test_metrics.py::test_fbeta [source]

To run tests please refer to this guide.

Computes the f_beta between preds and targets

beta determines the value of the fbeta applied, eps is there for numeric stability. If sigmoid=True, a sigmoid is applied to the predictions before comparing them to thresh then to the targets. See the F1 score wikipedia page for details on the fbeta score.

$${F_\beta} = (1+\beta^2)\frac{precision \cdot recall}{(\beta^2 \cdot precision) + recall}$$
preds = tensor([0.6, 0.8, 0.2, 0.4, 0.9]).view(1, 5) # TP =2, FP = 1, FN = 1
ys = tensor([1, 0, 0, 1, 1]).view(1, 5)
fbeta(preds, ys, thresh=0.5, sigmoid=False)

tensor(0.6667)

#### explained_variance[source][test]

explained_variance(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for explained_variance:

• pytest -sv tests/test_metrics.py::test_explained_variance [source]

To run tests please refer to this guide.

Explained variance between pred and targ.

$$Explained \ Variance = 1 - \frac{Var( targ - pred )}{Var( targ )}$$
preds = tensor([0.10, .20, .30, .40, .50])
ys = tensor([0.12, .17, .25, .44, .56]) # predictions are close to the truth
explained_variance(preds, ys)

tensor(0.9374)

#### r2_score[source][test]

r2_score(pred:Tensor, targ:Tensor) → Rank0Tensor

Tests found for r2_score:

• pytest -sv tests/test_metrics.py::test_r2_score [source]

To run tests please refer to this guide.

R2 score (coefficient of determination) between pred and targ.

$${R^2} = 1 - \frac{\sum( targ - pred )^2}{\sum( targ - \overline{targ})^2}$$

where $\overline{targ}$ is the mean of the targ tensor.

r2_score(preds, ys)

tensor(0.9351)

The following metrics are classes, don't forget to instantiate them when you pass them to a Learner.

### classRMSE[source][test]

RMSE() :: RegMetrics

No tests found for RMSE. To contribute a test please refer to this guide and this discussion.

Computes the root mean squared error.

### classExpRMSPE[source][test]

ExpRMSPE() :: RegMetrics

No tests found for ExpRMSPE. To contribute a test please refer to this guide and this discussion.

Computes the exponential of the root mean square error.

### classPrecision[source][test]

Precision(average:Optional[str]='binary', pos_label:int=1, eps:float=1e-09) :: CMScores

No tests found for Precision. To contribute a test please refer to this guide and this discussion.

Computes the Precision.

### classRecall[source][test]

Recall(average:Optional[str]='binary', pos_label:int=1, eps:float=1e-09) :: CMScores

No tests found for Recall. To contribute a test please refer to this guide and this discussion.

Computes the Recall.

### classFBeta[source][test]

FBeta(average:Optional[str]='binary', pos_label:int=1, eps:float=1e-09, beta:float=2) :: CMScores

No tests found for FBeta. To contribute a test please refer to this guide and this discussion.

Computes the Fbeta score.

### classR2Score[source][test]

R2Score() :: RegMetrics

No tests found for R2Score. To contribute a test please refer to this guide and this discussion.

Computes the R2 score (coefficient of determination).

### classExplainedVariance[source][test]

ExplainedVariance() :: RegMetrics

No tests found for ExplainedVariance. To contribute a test please refer to this guide and this discussion.

Computes the explained variance.

### classMatthewsCorreff[source][test]

MatthewsCorreff() :: ConfusionMatrix

No tests found for MatthewsCorreff. To contribute a test please refer to this guide and this discussion.

Computes the Matthews correlation coefficient.

### classKappaScore[source][test]

KappaScore(weights:Optional[str]=None) :: ConfusionMatrix

No tests found for KappaScore. To contribute a test please refer to this guide and this discussion.

Computes the rate of agreement (Cohens Kappa).

KappaScore supports linear and quadratic weights on the off-diagonal cells in the ConfusionMatrix, in addition to the default unweighted calculation treating all misclassifications as equally weighted. Leaving KappaScore's weights attribute as None returns the unweighted Kappa score. Updating weights to "linear" means off-diagonal ConfusionMatrix elements are weighted in linear proportion to their distance from the diagonal; "quadratic" means weights are squared proportional to their distance from the diagonal. Specify linear or quadratic weights, if using, by first creating an instance of the metric and then updating the weights attribute, similar to as follows:

kappa = KappaScore()
learn = cnn_learner(data, model, metrics=[error_rate, kappa])

### classConfusionMatrix[source][test]

ConfusionMatrix() :: Callback

No tests found for ConfusionMatrix. To contribute a test please refer to this guide and this discussion.

Computes the confusion matrix.

### classMultiLabelFbeta[source][test]

MultiLabelFbeta(beta=2, eps=1e-15, thresh=0.3, sigmoid=True, average='micro') :: Callback

No tests found for MultiLabelFbeta. To contribute a test please refer to this guide and this discussion.

Computes the fbeta score for multilabel classification

MultiLabelFbeta implements mutlilabel classification fbeta score similar to scikit-learn's as a LearnerCallback. Average options: ["micro", "macro", "weighted", "none"]. Intended to use with one-hot encoded targets with 1s and 0s.

show_doc(auc_roc_score, title_level=3)


### auc_roc_score[source][test]

auc_roc_score(input:Tensor, targ:Tensor)

No tests found for auc_roc_score. To contribute a test please refer to this guide and this discussion.

Computes the area under the receiver operator characteristic (ROC) curve using the trapezoid method. Restricted binary classification tasks.

auc_roc_score computes the AUC score for the ROC curve similarly to scikit-learn using the trapezoid method, effectively summarizing the curve information in a single number. See Wikipedia's page for more information on this.

jekyll_note("Instead of passing this method to the learner's metrics directly, make use of the AUROC() class.")

show_doc(roc_curve, title_level=3)


### roc_curve[source][test]

roc_curve(input:Tensor, targ:Tensor)

No tests found for roc_curve. To contribute a test please refer to this guide and this discussion.

Computes the receiver operator characteristic (ROC) curve by determining the true positive ratio (TPR) and false positive ratio (FPR) for various classification thresholds. Restricted binary classification tasks.

roc_curve generates the ROC curve similarly to scikit-learn. See Wikipedia's page for more information on the ROC curve.

jekyll_note("Instead of passing this method to the learner's metrics directly, make use of the AUROC() class.")

show_doc(AUROC, title_level=3)


### classAUROC[source][test]

AUROC() :: Callback

No tests found for AUROC. To contribute a test please refer to this guide and this discussion.

Computes the area under the curve (AUC) score based on the receiver operator characteristic (ROC) curve. Restricted to binary classification tasks.

AUROC creates a Callback for computing the AUC score for the ROC curve with auc_roc_score at the end of each epoch, given that averaging over batches is incorrect in case of the AUROC. See Wikipedia's page for more information on the AUROC.

## Creating your own metric¶

Creating a new metric can be as simple as creating a new function. If your metric is an average over the total number of elements in your dataset, just write the function that will compute it on a batch (taking pred and targ as arguments). It will then be automatically averaged over the batches (taking their different sizes into account).

Sometimes metrics aren't simple averages however. If we take the example of precision for instance, we have to divide the number of true positives by the number of predictions we made for that class. This isn't an average over the number of elements we have in the dataset, we only consider those where we made a positive prediction for a specific thing. Computing the precision for each batch, then averaging them will yield to a result that may be close to the real value, but won't be it exactly (and it really depends on how you deal with special case of 0 positive predictions).

This why in fastai, every metric is implemented as a callback. If you pass a regular function, the library transforms it to a proper callback called AverageCallback. The callback metrics are only called during the validation phase, and only for the following events:

• on_epoch_begin (for initialization)
• on_batch_begin (if we need to have a look at the input/target and maybe modify them)
• on_batch_end (to analyze the last results and update our computation)
• on_epoch_end(to wrap up the final result that should be added to last_metrics)

As an example, the following code is the exact implementation of the AverageMetric callback that transforms a function like accuracy into a metric callback.

class AverageMetric(Callback):
"Wrap a func in a callback for metrics computation."
def __init__(self, func):
# If it's a partial, use func.func
name = getattr(func,'func',func).__name__
self.func, self.name = func, name

def on_epoch_begin(self, **kwargs):
"Set the inner value to 0."
self.val, self.count = 0.,0

def on_batch_end(self, last_output, last_target, **kwargs):
"Update metric computation with last_output and last_target."
if not is_listy(last_target): last_target=[last_target]
self.count += last_target[0].size(0)
val = self.func(last_output, *last_target)
self.val += last_target[0].size(0) * val.detach().cpu()

def on_epoch_end(self, last_metrics, **kwargs):
"Set the final result in last_metrics."


Here add_metrics is a convenience function that will return the proper dictionary for us:

{'last_metrics': last_metrics + [self.val/self.count]}


And here is another example that properly computes the precision for a given class.

class Precision(Callback):

def on_epoch_begin(self, **kwargs):
self.correct, self.total = 0, 0

def on_batch_end(self, last_output, last_target, **kwargs):
preds = last_output.argmax(1)
self.correct += ((preds==0) * (last_target==0)).float().sum()
self.total += (preds==0).float().sum()

def on_epoch_end(self, last_metrics, **kwargs):


The following custom callback class example measures peak RAM usage during each epoch:

import tracemalloc
class TraceMallocMetric(Callback):
def __init__(self):
super().__init__()
self.name = "peak RAM"

def on_epoch_begin(self, **kwargs):
tracemalloc.start()

def on_epoch_end(self, last_metrics, **kwargs):
current, peak =  tracemalloc.get_traced_memory()
tracemalloc.stop()


To deploy it, you need to pass an instance of this custom metric in the metrics argument:

learn = cnn_learner(data, model, metrics=[accuracy, TraceMallocMetric()])
learn.fit_one_cycle(3, max_lr=1e-2)


And then the output changes to:

Total time: 00:54
epoch   train_loss  valid_loss  accuracy    peak RAM
1    0.333352    0.084342    0.973800    2395541.000000
2    0.096196    0.038386    0.988300    2342145.000000
3    0.048722    0.029234    0.990200    2342680.000000

As mentioner earlier, using the metrics argument with a custom metrics class is limited in the number of phases of the callback system it can access, it can only return one numerical value and as you can see its output is hardcoded to have 6 points of precision in the output, even if the number is an int.

To overcome these limitations callback classes should be used instead.

For example, the following class:

• uses phases not available for the metric classes
• it reports 3 columns, instead of just one
• its column report ints, instead of floats
import tracemalloc
class TraceMallocMultiColMetric(LearnerCallback):
_order=-20 # Needs to run before the recorder
def __init__(self, learn):
super().__init__(learn)
self.train_max = 0

def on_train_begin(self, **kwargs):

def on_batch_end(self, train, **kwargs):
# track max memory usage during the train phase
if train:
current, peak =  tracemalloc.get_traced_memory()
self.train_max = max(self.train_max, current)

def on_epoch_begin(self, **kwargs):
tracemalloc.start()

def on_epoch_end(self, last_metrics, **kwargs):
current, peak =  tracemalloc.get_traced_memory()
tracemalloc.stop()
return add_metrics(last_metrics, [current, self.train_max, peak])


Note, that it subclasses LearnerCallback and not Callback, since the former provides extra features not available in the latter.

Also _order=-20 is crucial - without it the custom columns will not be added - it tells the callback system to run this callback before the recorder system.

To deploy it, you need to pass the name of the class (not an instance!) of the class in the callback_fns argument. This is because the learn object doesn't exist yet, and it's required to instantiate TraceMallocMultiColMetric. The system will do it for us automatically as soon as the learn object has been created.

learn = cnn_learner(data, model, metrics=[accuracy], callback_fns=TraceMallocMultiColMetric)
learn.fit_one_cycle(3, max_lr=1e-2)


And then the output changes to:

Total time: 00:53
epoch   train_loss valid_loss   accuracy     used   max_used   peak
1   0.321233    0.068252    0.978600    156504  2408404   2419891
2   0.093551    0.032776    0.988500     79343  2408404   2348085
3   0.047178    0.025307    0.992100     79568  2408404   2342754

Another way to do the same is by using learn.callbacks.append, and this time we need to instantiate TraceMallocMultiColMetric with learn object which we now have, as it is called after the latter was created:

learn = cnn_learner(data, model, metrics=[accuracy])
learn.callbacks.append(TraceMallocMultiColMetric(learn))
learn.fit_one_cycle(3, max_lr=1e-2)


Configuring the custom metrics in the learn object sets them to run in all future fit-family calls. However, if you'd like to configure it for just one call, you can configure it directly inside fit or fit_one_cycle:

learn = cnn_learner(data, model, metrics=[accuracy])
learn.fit_one_cycle(3, max_lr=1e-2, callbacks=TraceMallocMultiColMetric(learn))


And to stress the differences:

• the callback_fns argument expects a classname or a list of those
• the callbacks argument expects an instance of a class or a list of those
• learn.callbacks.append expects a single instance of a class

For more examples, look inside fastai codebase and its test suite, search for classes that subclass either Callback, LearnerCallback and subclasses of those two.

Finally, while the above examples all add to the metrics, it's not a requirement. A callback can do anything it wants and it is not required to add its outcomes to the metrics printout.