Metrics

Definition of the metrics that can be used in training models

Core metric

This is where the function that converts scikit-learn metrics to fastai metrics is defined. You should skip this section unless you want to know all about the internals of fastai.

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AccumMetric

 AccumMetric (func, dim_argmax=None, activation='no', thresh=None,
              to_np=False, invert_arg=False, flatten=True, name=None,
              **kwargs)

Stores predictions and targets on CPU in accumulate to perform final calculations with func.

func is only applied to the accumulated predictions/targets when the value attribute is asked for (so at the end of a validation/training phase, in use with Learner and its Recorder).The signature of func should be inp,targ (where inp are the predictions of the model and targ the corresponding labels).

For classification problems with single label, predictions need to be transformed with a softmax then an argmax before being compared to the targets. Since a softmax doesn’t change the order of the numbers, we can just apply the argmax. Pass along dim_argmax to have this done by AccumMetric (usually -1 will work pretty well). If you need to pass to your metrics the probabilities and not the predictions, use softmax=True.

For classification problems with multiple labels, or if your targets are one-hot encoded, predictions may need to pass through a sigmoid (if it wasn’t included in your model) then be compared to a given threshold (to decide between 0 and 1), this is done by AccumMetric if you pass sigmoid=True and/or a value for thresh.

If you want to use a metric function sklearn.metrics, you will need to convert predictions and labels to numpy arrays with to_np=True. Also, scikit-learn metrics adopt the convention y_true, y_preds which is the opposite from us, so you will need to pass invert_arg=True to make AccumMetric do the inversion for you.

#For testing: a fake learner and a metric that isn't an average
@delegates()
class TstLearner(Learner):
    def __init__(self,dls=None,model=None,**kwargs): self.pred,self.xb,self.yb = None,None,None

def _l2_mean(x,y): return torch.sqrt((x.float()-y.float()).pow(2).mean())

#Go through a fake cycle with various batch sizes and computes the value of met
def compute_val(met, x1, x2):
    met.reset()
    vals = [0,6,15,20]
    learn = TstLearner()
    for i in range(3):
        learn.pred,learn.yb = x1[vals[i]:vals[i+1]],(x2[vals[i]:vals[i+1]],)
        met.accumulate(learn)
    return met.value

x1,x2 = torch.randn(20,5),torch.randn(20,5)
tst = AccumMetric(_l2_mean)
test_close(compute_val(tst, x1, x2), _l2_mean(x1, x2))
test_eq(torch.cat(tst.preds), x1.view(-1))
test_eq(torch.cat(tst.targs), x2.view(-1))

#test argmax
x1,x2 = torch.randn(20,5),torch.randint(0, 5, (20,))
tst = AccumMetric(_l2_mean, dim_argmax=-1)
test_close(compute_val(tst, x1, x2), _l2_mean(x1.argmax(dim=-1), x2))

#test thresh
x1,x2 = torch.randn(20,5),torch.randint(0, 2, (20,5)).bool()
tst = AccumMetric(_l2_mean, thresh=0.5)
test_close(compute_val(tst, x1, x2), _l2_mean((x1 >= 0.5), x2))

#test sigmoid
x1,x2 = torch.randn(20,5),torch.randn(20,5)
tst = AccumMetric(_l2_mean, activation=ActivationType.Sigmoid)
test_close(compute_val(tst, x1, x2), _l2_mean(torch.sigmoid(x1), x2))

#test to_np
x1,x2 = torch.randn(20,5),torch.randn(20,5)
tst = AccumMetric(lambda x,y: isinstance(x, np.ndarray) and isinstance(y, np.ndarray), to_np=True)
assert compute_val(tst, x1, x2)

#test invert_arg
x1,x2 = torch.randn(20,5),torch.randn(20,5)
tst = AccumMetric(lambda x,y: torch.sqrt(x.pow(2).mean()))
test_close(compute_val(tst, x1, x2), torch.sqrt(x1.pow(2).mean()))
tst = AccumMetric(lambda x,y: torch.sqrt(x.pow(2).mean()), invert_arg=True)
test_close(compute_val(tst, x1, x2), torch.sqrt(x2.pow(2).mean()))

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skm_to_fastai

 skm_to_fastai (func, is_class=True, thresh=None, axis=-1,
                activation=None, **kwargs)

Convert func from sklearn.metrics to a fastai metric

This is the quickest way to use a scikit-learn metric in a fastai training loop. is_class indicates if you are in a classification problem or not. In this case:

• leaving thresh to None indicates it’s a single-label classification problem and predictions will pass through an argmax over axis before being compared to the targets
• setting a value for thresh indicates it’s a multi-label classification problem and predictions will pass through a sigmoid (can be deactivated with sigmoid=False) and be compared to thresh before being compared to the targets

If is_class=False, it indicates you are in a regression problem, and predictions are compared to the targets without being modified. In all cases, kwargs are extra keyword arguments passed to func.

tst_single = skm_to_fastai(skm.precision_score)
x1,x2 = torch.randn(20,2),torch.randint(0, 2, (20,))
test_close(compute_val(tst_single, x1, x2), skm.precision_score(x2, x1.argmax(dim=-1)))

tst_multi = skm_to_fastai(skm.precision_score, thresh=0.2)
x1,x2 = torch.randn(20),torch.randint(0, 2, (20,))
test_close(compute_val(tst_multi, x1, x2), skm.precision_score(x2, torch.sigmoid(x1) >= 0.2))

tst_multi = skm_to_fastai(skm.precision_score, thresh=0.2, activation=ActivationType.No)
x1,x2 = torch.randn(20),torch.randint(0, 2, (20,))
test_close(compute_val(tst_multi, x1, x2), skm.precision_score(x2, x1 >= 0.2))

tst_reg = skm_to_fastai(skm.r2_score, is_class=False)
x1,x2 = torch.randn(20,5),torch.randn(20,5)
test_close(compute_val(tst_reg, x1, x2), skm.r2_score(x2.view(-1), x1.view(-1)))

test_close(tst_reg(x1, x2), skm.r2_score(x2.view(-1), x1.view(-1)))

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optim_metric

 optim_metric (f, argname, bounds, tol=0.01, do_neg=True, get_x=False)

Replace metric f with a version that optimizes argument argname

Single-label classification

Warning

All functions defined in this section are intended for single-label classification and targets that are not one-hot encoded. For multi-label problems or one-hot encoded targets, use the version suffixed with multi.

Warning

Many metrics in fastai are thin wrappers around sklearn functionality. However, sklearn metrics can handle python list strings, amongst other things, whereas fastai metrics work with PyTorch, and thus require tensors. The arguments that are passed to metrics are after all transformations, such as categories being converted to indices, have occurred. This means that when you pass a label of a metric, for instance, that you must pass indices, not strings. This can be converted with vocab.map_obj.

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accuracy

 accuracy (inp, targ, axis=-1)

Compute accuracy with targ when pred is bs * n_classes

#For testing
def change_targ(targ, n, c):
    idx = torch.randperm(len(targ))[:n]
    res = targ.clone()
    for i in idx: res[i] = (res[i]+random.randint(1,c-1))%c
    return res

x = torch.randn(4,5)
y = x.argmax(dim=1)
test_eq(accuracy(x,y), 1)
y1 = change_targ(y, 2, 5)
test_eq(accuracy(x,y1), 0.5)
test_eq(accuracy(x.unsqueeze(1).expand(4,2,5), torch.stack([y,y1], dim=1)), 0.75)

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error_rate

 error_rate (inp, targ, axis=-1)

1 - accuracy

x = torch.randn(4,5)
y = x.argmax(dim=1)
test_eq(error_rate(x,y), 0)
y1 = change_targ(y, 2, 5)
test_eq(error_rate(x,y1), 0.5)
test_eq(error_rate(x.unsqueeze(1).expand(4,2,5), torch.stack([y,y1], dim=1)), 0.25)

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top_k_accuracy

 top_k_accuracy (inp, targ, k=5, axis=-1)

Computes the Top-k accuracy (targ is in the top k predictions of inp)

x = torch.randn(6,5)
y = torch.arange(0,6)
test_eq(top_k_accuracy(x[:5],y[:5]), 1)
test_eq(top_k_accuracy(x, y), 5/6)

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APScoreBinary

 APScoreBinary (axis=-1, average='macro', pos_label=1, sample_weight=None)

Average Precision for single-label binary classification problems

See the scikit-learn documentation for more details.

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BalancedAccuracy

 BalancedAccuracy (axis=-1, sample_weight=None, adjusted=False)

Balanced Accuracy for single-label binary classification problems

See the scikit-learn documentation for more details.

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BrierScore

 BrierScore (axis=-1, sample_weight=None, pos_label=None)

Brier score for single-label classification problems

See the scikit-learn documentation for more details.

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CohenKappa

 CohenKappa (axis=-1, labels=None, weights=None, sample_weight=None)

Cohen kappa for single-label classification problems

See the scikit-learn documentation for more details.

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F1Score

 F1Score (axis=-1, labels=None, pos_label=1, average='binary',
          sample_weight=None)

F1 score for single-label classification problems

See the scikit-learn documentation for more details.

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FBeta

 FBeta (beta, axis=-1, labels=None, pos_label=1, average='binary',
        sample_weight=None)

FBeta score with beta for single-label classification problems

See the scikit-learn documentation for more details.

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HammingLoss

 HammingLoss (axis=-1, sample_weight=None)

Hamming loss for single-label classification problems

See the scikit-learn documentation for more details.

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Jaccard

 Jaccard (axis=-1, labels=None, pos_label=1, average='binary',
          sample_weight=None)

Jaccard score for single-label classification problems

See the scikit-learn documentation for more details.

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Precision

 Precision (axis=-1, labels=None, pos_label=1, average='binary',
            sample_weight=None)

Precision for single-label classification problems

See the scikit-learn documentation for more details.

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Recall

 Recall (axis=-1, labels=None, pos_label=1, average='binary',
         sample_weight=None)

Recall for single-label classification problems

See the scikit-learn documentation for more details.

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RocAuc

 RocAuc (axis=-1, average='macro', sample_weight=None, max_fpr=None,
         multi_class='ovr')

Area Under the Receiver Operating Characteristic Curve for single-label multiclass classification problems

See the scikit-learn documentation for more details.

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RocAucBinary

 RocAucBinary (axis=-1, average='macro', sample_weight=None, max_fpr=None,
               multi_class='raise')

Area Under the Receiver Operating Characteristic Curve for single-label binary classification problems

See the scikit-learn documentation for more details.

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MatthewsCorrCoef

 MatthewsCorrCoef (sample_weight=None, **kwargs)

Matthews correlation coefficient for single-label classification problems

See the scikit-learn documentation for more details.

Multi-label classification

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accuracy_multi

 accuracy_multi (inp, targ, thresh=0.5, sigmoid=True)

Compute accuracy when inp and targ are the same size.

#For testing
def change_1h_targ(targ, n):
    idx = torch.randperm(targ.numel())[:n]
    res = targ.clone().view(-1)
    for i in idx: res[i] = 1-res[i]
    return res.view(targ.shape)

x = torch.randn(4,5)
y = (torch.sigmoid(x) >= 0.5).byte()
test_eq(accuracy_multi(x,y), 1)
test_eq(accuracy_multi(x,1-y), 0)
y1 = change_1h_targ(y, 5)
test_eq(accuracy_multi(x,y1), 0.75)

#Different thresh
y = (torch.sigmoid(x) >= 0.2).byte()
test_eq(accuracy_multi(x,y, thresh=0.2), 1)
test_eq(accuracy_multi(x,1-y, thresh=0.2), 0)
y1 = change_1h_targ(y, 5)
test_eq(accuracy_multi(x,y1, thresh=0.2), 0.75)

#No sigmoid
y = (x >= 0.5).byte()
test_eq(accuracy_multi(x,y, sigmoid=False), 1)
test_eq(accuracy_multi(x,1-y, sigmoid=False), 0)
y1 = change_1h_targ(y, 5)
test_eq(accuracy_multi(x,y1, sigmoid=False), 0.75)

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APScoreMulti

 APScoreMulti (sigmoid=True, average='macro', pos_label=1,
               sample_weight=None)

Average Precision for multi-label classification problems

See the scikit-learn documentation for more details.

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BrierScoreMulti

 BrierScoreMulti (thresh=0.5, sigmoid=True, sample_weight=None,
                  pos_label=None)

Brier score for multi-label classification problems

See the scikit-learn documentation for more details.

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F1ScoreMulti

 F1ScoreMulti (thresh=0.5, sigmoid=True, labels=None, pos_label=1,
               average='macro', sample_weight=None)

F1 score for multi-label classification problems

See the scikit-learn documentation for more details.

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FBetaMulti

 FBetaMulti (beta, thresh=0.5, sigmoid=True, labels=None, pos_label=1,
             average='macro', sample_weight=None)

FBeta score with beta for multi-label classification problems

See the scikit-learn documentation for more details.

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HammingLossMulti

 HammingLossMulti (thresh=0.5, sigmoid=True, labels=None,
                   sample_weight=None)

Hamming loss for multi-label classification problems

See the scikit-learn documentation for more details.

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JaccardMulti

 JaccardMulti (thresh=0.5, sigmoid=True, labels=None, pos_label=1,
               average='macro', sample_weight=None)

Jaccard score for multi-label classification problems

See the scikit-learn documentation for more details.

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MatthewsCorrCoefMulti

 MatthewsCorrCoefMulti (thresh=0.5, sigmoid=True, sample_weight=None)

Matthews correlation coefficient for multi-label classification problems

See the scikit-learn documentation for more details.

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PrecisionMulti

 PrecisionMulti (thresh=0.5, sigmoid=True, labels=None, pos_label=1,
                 average='macro', sample_weight=None)

Precision for multi-label classification problems

See the scikit-learn documentation for more details.

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RecallMulti

 RecallMulti (thresh=0.5, sigmoid=True, labels=None, pos_label=1,
              average='macro', sample_weight=None)

Recall for multi-label classification problems

See the scikit-learn documentation for more details.

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RocAucMulti

 RocAucMulti (sigmoid=True, average='macro', sample_weight=None,
              max_fpr=None)

Area Under the Receiver Operating Characteristic Curve for multi-label binary classification problems

roc_auc_metric = RocAucMulti(sigmoid=False)
x,y = torch.tensor([np.arange(start=0, stop=0.2, step=0.04)]*20), torch.tensor([0, 0, 1, 1]).repeat(5)
assert compute_val(roc_auc_metric, x, y) == 0.5

/tmp/ipykernel_797/1899176771.py:2: UserWarning: Creating a tensor from a list of numpy.ndarrays is extremely slow. Please consider converting the list to a single numpy.ndarray with numpy.array() before converting to a tensor. (Triggered internally at  ../torch/csrc/utils/tensor_new.cpp:210.)
  x,y = torch.tensor([np.arange(start=0, stop=0.2, step=0.04)]*20), torch.tensor([0, 0, 1, 1]).repeat(5)

See the scikit-learn documentation for more details.

Regression

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mse

 mse (inp, targ)

Mean squared error between inp and targ.

x1,x2 = torch.randn(4,5),torch.randn(4,5)
test_close(mse(x1,x2), (x1-x2).pow(2).mean())

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rmse

 rmse (preds, targs)

Root mean squared error

x1,x2 = torch.randn(20,5),torch.randn(20,5)
test_eq(compute_val(rmse, x1, x2), torch.sqrt(F.mse_loss(x1,x2)))

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mae

 mae (inp, targ)

Mean absolute error between inp and targ.

x1,x2 = torch.randn(4,5),torch.randn(4,5)
test_eq(mae(x1,x2), torch.abs(x1-x2).mean())

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msle

 msle (inp, targ)

Mean squared logarithmic error between inp and targ.

x1,x2 = torch.randn(4,5),torch.randn(4,5)
x1,x2 = torch.relu(x1),torch.relu(x2)
test_close(msle(x1,x2), (torch.log(x1+1)-torch.log(x2+1)).pow(2).mean())

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exp_rmspe

 exp_rmspe (preds, targs)

Root mean square percentage error of the exponential of predictions and targets

x1,x2 = torch.randn(20,5),torch.randn(20,5)
test_eq(compute_val(exp_rmspe, x1, x2), torch.sqrt((((torch.exp(x2) - torch.exp(x1))/torch.exp(x2))**2).mean()))

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ExplainedVariance

 ExplainedVariance (sample_weight=None)

Explained variance between predictions and targets

See the scikit-learn documentation for more details.

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R2Score

 R2Score (sample_weight=None)

R2 score between predictions and targets

See the scikit-learn documentation for more details.

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PearsonCorrCoef

 PearsonCorrCoef (dim_argmax=None, activation='no', thresh=None,
                  to_np=False, invert_arg=False, flatten=True, name=None)

Pearson correlation coefficient for regression problem

See the scipy documentation for more details.

x = torch.randint(-999, 999,(20,))
y = torch.randint(-999, 999,(20,))
test_eq(compute_val(PearsonCorrCoef(), x, y), scs.pearsonr(x.view(-1), y.view(-1))[0])

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SpearmanCorrCoef

 SpearmanCorrCoef (dim_argmax=None, axis=0, nan_policy='propagate',
                   activation='no', thresh=None, to_np=False,
                   invert_arg=False, flatten=True, name=None)

Spearman correlation coefficient for regression problem

See the scipy documentation for more details.

x = torch.randint(-999, 999,(20,))
y = torch.randint(-999, 999,(20,))
test_eq(compute_val(SpearmanCorrCoef(), x, y), scs.spearmanr(x.view(-1), y.view(-1))[0])

Segmentation

from fastai.vision.all import *

model = resnet34()

x = cast(torch.rand(1,3,128,128), TensorImage)

type(model(x))

fastai.torch_core.TensorImage

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foreground_acc

 foreground_acc (inp, targ, bkg_idx=0, axis=1)

Computes non-background accuracy for multiclass segmentation

x = cast(torch.randn(4,5,3,3), TensorImage)
y = cast(x, TensorMask).argmax(dim=1)[:,None]
test_eq(foreground_acc(x,y), 1)
y[0] = 0 #the 0s are ignored so we get the same value
test_eq(foreground_acc(x,y), 1)

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Dice

 Dice (axis=1)

Dice coefficient metric for binary target in segmentation

x1 = cast(torch.randn(20,2,3,3), TensorImage)
x2 = cast(torch.randint(0, 2, (20, 3, 3)), TensorMask)
pred = x1.argmax(1)
inter = (pred*x2).float().sum().item()
union = (pred+x2).float().sum().item()
test_eq(compute_val(Dice(), x1, x2), 2*inter/union)

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DiceMulti

 DiceMulti (axis=1)

Averaged Dice metric (Macro F1) for multiclass target in segmentation

The DiceMulti method implements the “Averaged F1: arithmetic mean over harmonic means” described in this publication: https://arxiv.org/pdf/1911.03347.pdf

x1a = torch.ones(20,1,1,1)
x1b = torch.clone(x1a)*0.5
x1c = torch.clone(x1a)*0.3
x1 = torch.cat((x1a,x1b,x1c),dim=1)   # Prediction: 20xClass0
x2 = torch.zeros(20,1,1)              # Target: 20xClass0
test_eq(compute_val(DiceMulti(), x1, x2), 1.)

x2 = torch.ones(20,1,1)               # Target: 20xClass1
test_eq(compute_val(DiceMulti(), x1, x2), 0.)

x2a = torch.zeros(10,1,1)
x2b = torch.ones(5,1,1)
x2c = torch.ones(5,1,1) * 2
x2 = torch.cat((x2a,x2b,x2c),dim=0)   # Target: 10xClass0, 5xClass1, 5xClass2
dice1 = (2*10)/(2*10+10)              # Dice: 2*TP/(2*TP+FP+FN)
dice2 = 0
dice3 = 0
test_eq(compute_val(DiceMulti(), x1, x2), (dice1+dice2+dice3)/3)

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JaccardCoeff

 JaccardCoeff (axis=1)

Implementation of the Jaccard coefficient that is lighter in RAM

x1 = cast(torch.randn(20,2,3,3), TensorImage)
x2 = cast(torch.randint(0, 2, (20, 3, 3)), TensorMask)
pred = x1.argmax(1)
inter = (pred*x2).float().sum().item()
union = (pred+x2).float().sum().item()
test_eq(compute_val(JaccardCoeff(), x1, x2), inter/(union-inter))

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JaccardCoeffMulti

 JaccardCoeffMulti (axis=1)

Averaged Jaccard coefficient metric (mIoU) for multiclass target in segmentation

x1a = torch.ones(20,1,1,1)
x1b = torch.clone(x1a)*0.5
x1c = torch.clone(x1a)*0.3
x1 = torch.cat((x1a,x1b,x1c), dim=1)   # Prediction: 20xClass0
x2 = torch.zeros(20,1,1)              # Target: 20xClass0
test_eq(compute_val(JaccardCoeffMulti(), x1, x2), 1.)

x2 = torch.ones(20,1,1)               # Target: 20xClass1
test_eq(compute_val(JaccardCoeffMulti(), x1, x2), 0.)

x2a = torch.zeros(10,1,1)
x2b = torch.ones(5,1,1)
x2c = torch.ones(5,1,1) * 2
x2 = torch.cat((x2a,x2b,x2c), dim=0)   # Target: 10xClass0, 5xClass1, 5xClass2
jcrd1 = 10/(10+10)              # Jaccard: TP/(TP+FP+FN)
jcrd2 = 0
jcrd3 = 0
test_eq(compute_val(JaccardCoeffMulti(), x1, x2), (jcrd1+jcrd2+jcrd3)/3)

NLP

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CorpusBLEUMetric

 CorpusBLEUMetric (vocab_sz=5000, axis=-1)

Blueprint for defining a metric

def create_vcb_emb(pred, targ):
    # create vocab "embedding" for predictions
    vcb_sz = max(torch.unique(torch.cat([pred, targ])))+1
    pred_emb=torch.zeros(pred.size()[0], pred.size()[1] ,vcb_sz)
    for i,v in enumerate(pred):
        pred_emb[i].scatter_(1, v.view(len(v),1),1)
    return pred_emb

def compute_bleu_val(met, x1, x2):
    met.reset()
    learn = TstLearner()
    learn.training=False    
    for i in range(len(x1)): 
        learn.pred,learn.yb = x1, (x2,)
        met.accumulate(learn)
    return met.value

targ = torch.tensor([[1,2,3,4,5,6,1,7,8]]) 
pred = torch.tensor([[1,9,3,4,5,6,1,10,8]])
pred_emb = create_vcb_emb(pred, targ)
test_close(compute_bleu_val(CorpusBLEUMetric(), pred_emb, targ), 0.48549)

targ = torch.tensor([[1,2,3,4,5,6,1,7,8],[1,2,3,4,5,6,1,7,8]]) 
pred = torch.tensor([[1,9,3,4,5,6,1,10,8],[1,9,3,4,5,6,1,10,8]])
pred_emb = create_vcb_emb(pred, targ)
test_close(compute_bleu_val(CorpusBLEUMetric(), pred_emb, targ), 0.48549)

The BLEU metric was introduced in this article to come up with a way to evaluate the performance of translation models. It’s based on the precision of n-grams in your prediction compared to your target. See the fastai NLP course BLEU notebook for a more detailed description of BLEU.

The smoothing used in the precision calculation is the same as in SacreBLEU, which in turn is “method 3” from the Chen & Cherry, 2014 paper.

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Perplexity

 Perplexity ()

Perplexity (exponential of cross-entropy loss) for Language Models

x1,x2 = torch.randn(20,5),torch.randint(0, 5, (20,))
tst = perplexity
tst.reset()
vals = [0,6,15,20]
learn = TstLearner()
for i in range(3): 
    learn.yb = (x2[vals[i]:vals[i+1]],)
    learn.loss = F.cross_entropy(x1[vals[i]:vals[i+1]],x2[vals[i]:vals[i+1]])
    tst.accumulate(learn)
test_close(tst.value, torch.exp(F.cross_entropy(x1,x2)))

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LossMetric

 LossMetric (attr, nm=None)

Create a metric from loss_func.attr named nm

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LossMetrics

 LossMetrics (attrs, nms=None)

List of LossMetric for each of attrs and nms

class CombineL1L2(Module):
    def forward(self, out, targ):
        self.l1 = F.l1_loss(out, targ)
        self.l2 = F.mse_loss(out, targ)
        return self.l1+self.l2

learn = synth_learner(metrics=LossMetrics('l1,l2'))
learn.loss_func = CombineL1L2()
learn.fit(2)

epoch	train_loss	valid_loss	l1	l2	time
0	13.255276	15.401798	3.086604	12.315195	00:00
1	11.667193	11.073782	2.547795	8.525988	00:00