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Creates a `Head` for regression using the `mean_squared_error` loss.

Inherits From: `Head`

The loss is the weighted sum over all input dimensions. Namely, if the input labels have shape `[batch_size, label_dimension]`, the loss is the weighted sum over both `batch_size` and `label_dimension`.

The head expects `logits` with shape `[D0, D1, ... DN, label_dimension]`. In many applications, the shape is `[batch_size, label_dimension]`.

The `labels` shape must match `logits`, namely `[D0, D1, ... DN, label_dimension]`. If `label_dimension=1`, shape `[D0, D1, ... DN]` is also supported.

If `weight_column` is specified, weights must be of shape `[D0, D1, ... DN]`, `[D0, D1, ... DN, 1]` or `[D0, D1, ... DN, label_dimension]`.

Supports custom `loss_fn`. `loss_fn` takes `(labels, logits)` or `(labels, logits, features, loss_reduction)` as arguments and returns unreduced loss with shape `[D0, D1, ... DN, label_dimension]`.

Also supports custom `inverse_link_fn`, also known as 'mean function'. `inverse_link_fn` is only used in `PREDICT` mode. It takes `logits` as argument and returns predicted values. This function is the inverse of the link function defined in https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function Namely, for poisson regression, set `inverse_link_fn=tf.exp`.

#### Usage:

````head = tf.estimator.RegressionHead()`
`logits = np.array(((45,), (41,),), dtype=np.float32)`
`labels = np.array(((43,), (44,),), dtype=np.int32)`
`features = {'x': np.array(((42,),), dtype=np.float32)}`
`# expected_loss = weighted_loss / batch_size`
`#               = (43-45)^2 + (44-41)^2 / 2 = 6.50`
`loss = head.loss(labels, logits, features=features)`
`print('{:.2f}'.format(loss.numpy()))`
`6.50`
`eval_metrics = head.metrics()`
`updated_metrics = head.update_metrics(`
`  eval_metrics, features, logits, labels)`
`for k in sorted(updated_metrics):`
` print('{} : {:.2f}'.format(k, updated_metrics[k].result().numpy()))`
`  average_loss : 6.50`
`  label/mean : 43.50`
`  prediction/mean : 43.00`
`preds = head.predictions(logits)`
`print(preds['predictions'])`
`tf.Tensor(`
`  [[45.]`
`   [41.]], shape=(2, 1), dtype=float32)`
```

Usage with a canned estimator:

``````my_head = tf.estimator.RegressionHead()
my_estimator = tf.estimator.DNNEstimator(
hidden_units=...,
feature_columns=...)
``````

It can also be used with a custom `model_fn`. Example:

``````def _my_model_fn(features, labels, mode):
logits = tf.keras.Model(...)(features)

features=features,
mode=mode,
labels=labels,
logits=logits)

my_estimator = tf.estimator.Estimator(model_fn=_my_model_fn)
``````

`weight_column` A string or a `NumericColumn` created by `tf.feature_column.numeric_column` defining feature column representing weights. It is used to down weight or boost examples during training. It will be multiplied by the loss of the example.
`label_dimension` Number of regression labels per example. This is the size of the last dimension of the labels `Tensor` (typically, this has shape `[batch_size, label_dimension]`).
`loss_reduction` One of `tf.losses.Reduction` except `NONE`. Decides how to reduce training loss over batch and label dimension. Defaults to `SUM_OVER_BATCH_SIZE`, namely weighted sum of losses divided by `batch_size * label_dimension`.
`loss_fn` Optional loss function. Defaults to `mean_squared_error`.
`inverse_link_fn` Optional inverse link function, also known as 'mean function'. Defaults to identity.
`name` name of the head. If provided, summary and metrics keys will be suffixed by `"/" + name`. Also used as `name_scope` when creating ops.

`logits_dimension` See `base_head.Head` for details.
`loss_reduction` See `base_head.Head` for details.
`name` See `base_head.Head` for details.

## Methods

### `create_estimator_spec`

View source

Returns `EstimatorSpec` that a model_fn can return.

It is recommended to pass all args via name.

Args
`features` Input `dict` mapping string feature names to `Tensor` or `SparseTensor` objects containing the values for that feature in a minibatch. Often to be used to fetch example-weight tensor.
`mode` Estimator's `ModeKeys`.
`logits` Logits `Tensor` to be used by the head.
`labels` Labels `Tensor`, or `dict` mapping string label names to `Tensor` objects of the label values.
`optimizer` An `tf.keras.optimizers.Optimizer` instance to optimize the loss in TRAIN mode. Namely, sets ```train_op = optimizer.get_updates(loss, trainable_variables)```, which updates variables to minimize `loss`.
`trainable_variables` A list or tuple of `Variable` objects to update to minimize `loss`. In Tensorflow 1.x, by default these are the list of variables collected in the graph under the key `GraphKeys.TRAINABLE_VARIABLES`. As Tensorflow 2.x doesn't have collections and GraphKeys, trainable_variables need to be passed explicitly here.
`train_op_fn` Function that takes a scalar loss `Tensor` and returns an op to optimize the model with the loss in TRAIN mode. Used if `optimizer` is `None`. Exactly one of `train_op_fn` and `optimizer` must be set in TRAIN mode. By default, it is `None` in other modes. If you want to optimize loss yourself, you can pass `lambda _: tf.no_op()` and then use `EstimatorSpec.loss` to compute and apply gradients.
`update_ops` A list or tuple of update ops to be run at training time. For example, layers such as BatchNormalization create mean and variance update ops that need to be run at training time. In Tensorflow 1.x, these are thrown into an UPDATE_OPS collection. As Tensorflow 2.x doesn't have collections, update_ops need to be passed explicitly here.
`regularization_losses` A list of additional scalar losses to be added to the training loss, such as regularization losses.

Returns
`EstimatorSpec`.

### `loss`

View source

Return predictions based on keys. See `base_head.Head` for details.

### `metrics`

View source

Creates metrics. See `base_head.Head` for details.

### `predictions`

View source

Return predictions based on keys.

See `base_head.Head` for details.

Args
`logits` logits `Tensor` with shape `[D0, D1, ... DN, logits_dimension]`. For many applications, the shape is `[batch_size, logits_dimension]`.

Returns
A dict of predictions.

### `update_metrics`

View source

Updates eval metrics. See `base_head.Head` for details.

[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]