treex.losses.huber
Huber (Loss)
Computes the Huber loss between target and predictions.
For each value x in error = target - preds:
loss =
\begin{cases}
\ 0.5 \times x^2,\hskip8em\text{if } |x|\leq d\\
0.5 \times d^2 + d \times (|x| - d),\hskip1.7em \text{otherwise}
\end{cases}
where d is delta. See: https://en.wikipedia.org/wiki/Huber_loss
Usage:
target = jnp.array([[0, 1], [0, 0]])
preds = jnp.array([[0.6, 0.4], [0.4, 0.6]])
# Using 'auto'/'sum_over_batch_size' reduction type.
huber_loss = tx.losses.Huber()
assert huber_loss(target, preds) == 0.155
# Calling with 'sample_weight'.
assert (
huber_loss(target, preds, sample_weight=jnp.array([0.8, 0.2])) == 0.08500001
)
# Using 'sum' reduction type.
huber_loss = tx.losses.Huber(
reduction=tx.losses.Reduction.SUM
)
assert huber_loss(target, preds) == 0.31
# Using 'none' reduction type.
huber_loss = tx.losses.Huber(
reduction=tx.losses.Reduction.NONE
)
assert jnp.equal(huber_loss(target, preds), jnp.array([0.18, 0.13000001])).all()
model = elegy.Model(
module_fn,
loss=tx.losses.Huber(delta=1.0),
metrics=elegy.metrics.Mean(),
)
Source code in treex/losses/huber.py
class Huber(Loss):
r"""
Computes the Huber loss between target and predictions.
For each value x in error = target - preds:
$$
loss =
\begin{cases}
\ 0.5 \times x^2,\hskip8em\text{if } |x|\leq d\\
0.5 \times d^2 + d \times (|x| - d),\hskip1.7em \text{otherwise}
\end{cases}
$$
where d is delta. See: https://en.wikipedia.org/wiki/Huber_loss
Usage:
```python
target = jnp.array([[0, 1], [0, 0]])
preds = jnp.array([[0.6, 0.4], [0.4, 0.6]])
# Using 'auto'/'sum_over_batch_size' reduction type.
huber_loss = tx.losses.Huber()
assert huber_loss(target, preds) == 0.155
# Calling with 'sample_weight'.
assert (
huber_loss(target, preds, sample_weight=jnp.array([0.8, 0.2])) == 0.08500001
)
# Using 'sum' reduction type.
huber_loss = tx.losses.Huber(
reduction=tx.losses.Reduction.SUM
)
assert huber_loss(target, preds) == 0.31
# Using 'none' reduction type.
huber_loss = tx.losses.Huber(
reduction=tx.losses.Reduction.NONE
)
assert jnp.equal(huber_loss(target, preds), jnp.array([0.18, 0.13000001])).all()
```
Usage with the Elegy API:
```python
model = elegy.Model(
module_fn,
loss=tx.losses.Huber(delta=1.0),
metrics=elegy.metrics.Mean(),
)
```
"""
def __init__(
self,
delta: float = 1.0,
reduction: tp.Optional[Reduction] = None,
weight: tp.Optional[float] = None,
on: tp.Optional[types.IndexLike] = None,
**kwargs
):
"""
Initializes `Mean` class.
Arguments:
delta: (Optional) Defaults to 1.0. A float, the point where the Huber loss function changes from a quadratic to linear.
reduction: (Optional) Type of `tx.losses.Reduction` to apply to
loss. Default value is `SUM_OVER_BATCH_SIZE`. For almost all cases
this defaults to `SUM_OVER_BATCH_SIZE`.
weight: Optional weight contribution for the total loss. Defaults to `1`.
on: A string or integer, or iterable of string or integers, that
indicate how to index/filter the `target` and `preds`
arguments before passing them to `call`. For example if `on = "a"` then
`target = target["a"]`. If `on` is an iterable
the structures will be indexed iteratively, for example if `on = ["a", 0, "b"]`
then `target = target["a"][0]["b"]`, same for `preds`. For more information
check out [Keras-like behavior](https://poets-ai.github.io/elegy/guides/modules-losses-metrics/#keras-like-behavior).
"""
self.delta = delta
return super().__init__(reduction=reduction, weight=weight, on=on, **kwargs)
def call(
self,
target: jnp.ndarray,
preds: jnp.ndarray,
sample_weight: tp.Optional[
jnp.ndarray
] = None, # not used, __call__ handles it, left for documentation purposes.
) -> jnp.ndarray:
"""
Invokes the `Huber` instance.
Arguments:
target: Ground truth values. shape = `[batch_size, d0, .. dN]`, except
sparse loss functions such as sparse categorical crossentropy where
shape = `[batch_size, d0, .. dN-1]`
preds: The predicted values. shape = `[batch_size, d0, .. dN]`
sample_weight: Optional `sample_weight` acts as a
coefficient for the loss. If a scalar is provided, then the loss is
simply scaled by the given value. If `sample_weight` is a tensor of size
`[batch_size]`, then the total loss for each sample of the batch is
rescaled by the corresponding element in the `sample_weight` vector. If
the shape of `sample_weight` is `[batch_size, d0, .. dN-1]` (or can be
broadcasted to this shape), then each loss element of `preds` is scaled
by the corresponding value of `sample_weight`. (Note on`dN-1`: all loss
functions reduce by 1 dimension, usually axis=-1.)
Returns:
Weighted loss float `Tensor`. If `reduction` is `NONE`, this has
shape `[batch_size, d0, .. dN-1]`; otherwise, it is scalar. (Note `dN-1`
because all loss functions reduce by 1 dimension, usually axis=-1.)
Raises:
ValueError: If the shape of `sample_weight` is invalid.
"""
return huber(target, preds, self.delta)
__init__(self, delta=1.0, reduction=None, weight=None, on=None, **kwargs)
special
Initializes Mean class.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
delta |
float |
(Optional) Defaults to 1.0. A float, the point where the Huber loss function changes from a quadratic to linear. |
1.0 |
reduction |
Optional[treex.losses.loss.Reduction] |
(Optional) Type of |
None |
weight |
Optional[float] |
Optional weight contribution for the total loss. Defaults to |
None |
on |
Union[str, int, Sequence[Union[str, int]]] |
A string or integer, or iterable of string or integers, that
indicate how to index/filter the |
None |
Source code in treex/losses/huber.py
def __init__(
self,
delta: float = 1.0,
reduction: tp.Optional[Reduction] = None,
weight: tp.Optional[float] = None,
on: tp.Optional[types.IndexLike] = None,
**kwargs
):
"""
Initializes `Mean` class.
Arguments:
delta: (Optional) Defaults to 1.0. A float, the point where the Huber loss function changes from a quadratic to linear.
reduction: (Optional) Type of `tx.losses.Reduction` to apply to
loss. Default value is `SUM_OVER_BATCH_SIZE`. For almost all cases
this defaults to `SUM_OVER_BATCH_SIZE`.
weight: Optional weight contribution for the total loss. Defaults to `1`.
on: A string or integer, or iterable of string or integers, that
indicate how to index/filter the `target` and `preds`
arguments before passing them to `call`. For example if `on = "a"` then
`target = target["a"]`. If `on` is an iterable
the structures will be indexed iteratively, for example if `on = ["a", 0, "b"]`
then `target = target["a"][0]["b"]`, same for `preds`. For more information
check out [Keras-like behavior](https://poets-ai.github.io/elegy/guides/modules-losses-metrics/#keras-like-behavior).
"""
self.delta = delta
return super().__init__(reduction=reduction, weight=weight, on=on, **kwargs)
call(self, target, preds, sample_weight=None)
Invokes the Huber instance.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
target |
ndarray |
Ground truth values. shape = |
required |
preds |
ndarray |
The predicted values. shape = |
required |
sample_weight |
Optional[jax._src.numpy.lax_numpy.ndarray] |
Optional |
None |
Returns:
| Type | Description |
|---|---|
ndarray |
Weighted loss float |
Exceptions:
| Type | Description |
|---|---|
ValueError |
If the shape of |
Source code in treex/losses/huber.py
def call(
self,
target: jnp.ndarray,
preds: jnp.ndarray,
sample_weight: tp.Optional[
jnp.ndarray
] = None, # not used, __call__ handles it, left for documentation purposes.
) -> jnp.ndarray:
"""
Invokes the `Huber` instance.
Arguments:
target: Ground truth values. shape = `[batch_size, d0, .. dN]`, except
sparse loss functions such as sparse categorical crossentropy where
shape = `[batch_size, d0, .. dN-1]`
preds: The predicted values. shape = `[batch_size, d0, .. dN]`
sample_weight: Optional `sample_weight` acts as a
coefficient for the loss. If a scalar is provided, then the loss is
simply scaled by the given value. If `sample_weight` is a tensor of size
`[batch_size]`, then the total loss for each sample of the batch is
rescaled by the corresponding element in the `sample_weight` vector. If
the shape of `sample_weight` is `[batch_size, d0, .. dN-1]` (or can be
broadcasted to this shape), then each loss element of `preds` is scaled
by the corresponding value of `sample_weight`. (Note on`dN-1`: all loss
functions reduce by 1 dimension, usually axis=-1.)
Returns:
Weighted loss float `Tensor`. If `reduction` is `NONE`, this has
shape `[batch_size, d0, .. dN-1]`; otherwise, it is scalar. (Note `dN-1`
because all loss functions reduce by 1 dimension, usually axis=-1.)
Raises:
ValueError: If the shape of `sample_weight` is invalid.
"""
return huber(target, preds, self.delta)
huber(target, preds, delta)
Computes the Huber loss between target and predictions.
For each value x in error = target - preds:
loss =
\begin{cases}
\ 0.5 \times x^2,\hskip8em\text{if } |x|\leq d\\
0.5 \times d^2 + d \times (|x| - d),\hskip1.7em \text{otherwise}
\end{cases}
where d is delta. See: https://en.wikipedia.org/wiki/Huber_loss
Usage:
rng = jax.random.PRNGKey(42)
target = jax.random.randint(rng, shape=(2, 3), minval=0, maxval=2)
preds = jax.random.uniform(rng, shape=(2, 3))
loss = tx.losses.huber(target, preds, delta=1.0)
assert loss.shape == (2,)
preds = preds.astype(float)
target = target.astype(float)
delta = 1.0
error = jnp.subtract(preds, target)
abs_error = jnp.abs(error)
quadratic = jnp.minimum(abs_error, delta)
linear = jnp.subtract(abs_error, quadratic)
assert jnp.array_equal(loss, jnp.mean(
jnp.add(
jnp.multiply(
0.5,
jnp.multiply(quadratic, quadratic)
),
jnp.multiply(delta, linear)), axis=-1
))
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
target |
ndarray |
Ground truth values. shape = |
required |
preds |
ndarray |
The predicted values. shape = |
required |
delta |
float |
A float, the point where the Huber loss function changes from a quadratic to linear. |
required |
Returns:
| Type | Description |
|---|---|
ndarray |
huber loss Values. If reduction is NONE, this has |
shape [batch_size, d0, .. dN-1]; otherwise, it is scalar.
(Note dN-1 because all loss functions reduce by 1 dimension, usually axis=-1.)
Source code in treex/losses/huber.py
def huber(target: jnp.ndarray, preds: jnp.ndarray, delta: float) -> jnp.ndarray:
r"""
Computes the Huber loss between target and predictions.
For each value x in error = target - preds:
$$
loss =
\begin{cases}
\ 0.5 \times x^2,\hskip8em\text{if } |x|\leq d\\
0.5 \times d^2 + d \times (|x| - d),\hskip1.7em \text{otherwise}
\end{cases}
$$
where d is delta. See: https://en.wikipedia.org/wiki/Huber_loss
Usage:
```python
rng = jax.random.PRNGKey(42)
target = jax.random.randint(rng, shape=(2, 3), minval=0, maxval=2)
preds = jax.random.uniform(rng, shape=(2, 3))
loss = tx.losses.huber(target, preds, delta=1.0)
assert loss.shape == (2,)
preds = preds.astype(float)
target = target.astype(float)
delta = 1.0
error = jnp.subtract(preds, target)
abs_error = jnp.abs(error)
quadratic = jnp.minimum(abs_error, delta)
linear = jnp.subtract(abs_error, quadratic)
assert jnp.array_equal(loss, jnp.mean(
jnp.add(
jnp.multiply(
0.5,
jnp.multiply(quadratic, quadratic)
),
jnp.multiply(delta, linear)), axis=-1
))
```
Arguments:
target: Ground truth values. shape = `[batch_size, d0, .. dN]`.
preds: The predicted values. shape = `[batch_size, d0, .. dN]`.
delta: A float, the point where the Huber loss function changes from a quadratic to linear.
Returns:
huber loss Values. If reduction is NONE, this has
shape [batch_size, d0, .. dN-1]; otherwise, it is scalar.
(Note dN-1 because all loss functions reduce by 1 dimension, usually axis=-1.)
"""
preds = preds.astype(float)
target = target.astype(float)
delta = float(delta)
error = jnp.subtract(preds, target)
abs_error = jnp.abs(error)
quadratic = jnp.minimum(abs_error, delta)
linear = jnp.subtract(abs_error, quadratic)
return jnp.mean(
jnp.add(
jnp.multiply(0.5, jnp.multiply(quadratic, quadratic)),
jnp.multiply(delta, linear),
),
axis=-1,
)