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Use this crossentropy loss function when there are two or more label classes and if you want to handle class imbalance without using class_weights. We expect labels to be provided in a one_hot representation.

According to Lin et al., 2018, it helps to apply a focal factor to down-weight easy examples and focus more on hard examples. The general formula for the focal loss (FL) is as follows:

FL(p_t) = (1 - p_t)^gamma * log(p_t)

where p_t is defined as follows: p_t = output if y_true == 1, else 1 - output

(1 - p_t)^gamma is the modulating_factor, where gamma is a focusing parameter. When gamma = 0, there is no focal effect on the cross entropy. gamma reduces the importance given to simple examples in a smooth manner.

The authors use alpha-balanced variant of focal loss (FL) in the paper: FL(p_t) = -alpha * (1 - p_t)^gamma * log(p_t)

where alpha is the weight factor for the classes. If alpha = 1, the loss won't be able to handle class imbalance properly as all classes will have the same weight. This can be a constant or a list of constants. If alpha is a list, it must have the same length as the number of classes.

The formula above can be generalized to: FL(p_t) = alpha * (1 - p_t)^gamma * CrossEntropy(y_true, y_pred)

where minus comes from CrossEntropy(y_true, y_pred) (CE).

Extending this to multi-class case is straightforward: FL(p_t) = alpha * (1 - p_t) ** gamma * CategoricalCE(y_true, y_pred)

In the snippet below, there is num_classes floating pointing values per example. The shape of both y_pred and y_true are (batch_size, num_classes).

Usage

loss_categorical_focal_crossentropy(
  y_true,
  y_pred,
  alpha = 0.25,
  gamma = 2,
  from_logits = FALSE,
  label_smoothing = 0,
  axis = -1L,
  ...,
  reduction = "sum_over_batch_size",
  name = "categorical_focal_crossentropy",
  dtype = NULL
)

Arguments

y_true

Tensor of one-hot true targets.

y_pred

Tensor of predicted targets.

alpha

A weight balancing factor for all classes, default is 0.25 as mentioned in the reference. It can be a list of floats or a scalar. In the multi-class case, alpha may be set by inverse class frequency by using compute_class_weight from sklearn.utils.

gamma

A focusing parameter, default is 2.0 as mentioned in the reference. It helps to gradually reduce the importance given to simple examples in a smooth manner. When gamma = 0, there is no focal effect on the categorical crossentropy.

from_logits

Whether output is expected to be a logits tensor. By default, we consider that output encodes a probability distribution.

label_smoothing

Float in [0, 1]. When > 0, label values are smoothed, meaning the confidence on label values are relaxed. For example, if 0.1, use 0.1 / num_classes for non-target labels and 0.9 + 0.1 / num_classes for target labels.

axis

The axis along which to compute crossentropy (the features axis). Defaults to -1.

...

For forward/backward compatability.

reduction

Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or NULL.

name

Optional name for the loss instance.

dtype

The dtype of the loss's computations. Defaults to NULL, which means using config_floatx(). config_floatx() is a "float32" unless set to different value (via config_set_floatx()). If a keras$DTypePolicy is provided, then the compute_dtype will be utilized.

Value

Categorical focal crossentropy loss value.

Examples

y_true <- rbind(c(0, 1, 0), c(0, 0, 1))
y_pred <- rbind(c(0.05, 0.95, 0), c(0.1, 0.8, 0.1))
loss <- loss_categorical_focal_crossentropy(y_true, y_pred)
loss

## tf.Tensor([3.20583090e-05 4.66273481e-01], shape=(2), dtype=float64)

Standalone usage:

y_true <- rbind(c(0, 1, 0), c(0, 0, 1))
y_pred <- rbind(c(0.05, 0.95, 0), c(0.1, 0.8, 0.1))
# Using 'auto'/'sum_over_batch_size' reduction type.
cce <- loss_categorical_focal_crossentropy()
cce(y_true, y_pred)

## tf.Tensor(0.23315276, shape=(), dtype=float32)

# Calling with 'sample_weight'.
cce(y_true, y_pred, sample_weight = op_array(c(0.3, 0.7)))

## tf.Tensor(0.16320053, shape=(), dtype=float32)

# Using 'sum' reduction type.
cce <- loss_categorical_focal_crossentropy(reduction = "sum")
cce(y_true, y_pred)

## tf.Tensor(0.46630552, shape=(), dtype=float32)

# Using 'none' reduction type.
cce <- loss_categorical_focal_crossentropy(reduction = NULL)
cce(y_true, y_pred)

## tf.Tensor([3.2058331e-05 4.6627346e-01], shape=(2), dtype=float32)

Usage with the compile() API:

model %>% compile(
  optimizer = 'adam',
  loss = loss_categorical_focal_crossentropy())