PairwiseMeanSquaredError

[source]

PairwiseMeanSquaredError class

keras_rs.losses.PairwiseMeanSquaredError(temperature: float = 1.0, **kwargs: Any)

Computes pairwise mean squared error between true labels and predicted scores. This loss function is designed for ranking tasks, where the goal is to correctly order items within each list. It computes the loss by comparing pairs of items within each list, penalizing cases where an item with a higher true label has a lower predicted score than an item with a lower true label.

For each list of predicted scores s in y_pred and the corresponding list of true labels y in y_true, the loss is computed as follows:

loss = sum_{i} sum_{j} I(y_i > y_j) * (s_i - s_j)^2

where:

• y_i and y_j are the true labels of items i and j, respectively.
• s_i and s_j are the predicted scores of items i and j, respectively.
• I(y_i > y_j) is an indicator function that equals 1 if y_i > y_j, and 0 otherwise.
• (s_i - s_j)^2 is the squared difference between the predicted scores of items i and j, which penalizes discrepancies between the predicted order of items relative to their true order.

Arguments

• 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", "mean", "mean_with_sample_weight" or None. "sum" sums the loss, "sum_over_batch_size" and "mean" sum the loss and divide by the sample size, and "mean_with_sample_weight" sums the loss and divides by the sum of the sample weights. "none" and None perform no aggregation. Defaults to "sum_over_batch_size".
• name: Optional name for the loss instance.
• dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

Examples

With compile() API:

model.compile(
    loss=keras_rs.losses.PairwiseMeanSquaredError(),
    ...
)

As a standalone function with unbatched inputs:

>>> y_true = np.array([1.0, 0.0, 1.0, 3.0, 2.0])
>>> y_pred = np.array([1.0, 3.0, 2.0, 4.0, 0.8])
>>> pairwise_mse = keras_rs.losses.PairwiseMeanSquaredError()
>>> pairwise_mse(y_true=y_true, y_pred=y_pred)
>>> 19.10400

With batched inputs using default 'auto'/'sum_over_batch_size' reduction:

>>> y_true = np.array([[1.0, 0.0, 1.0, 3.0], [0.0, 1.0, 2.0, 3.0]])
>>> y_pred = np.array([[1.0, 3.0, 2.0, 4.0], [1.0, 1.8, 2.0, 3.0]])
>>> pairwise_mse = keras_rs.losses.PairwiseMeanSquaredError()
>>> pairwise_mse(y_true=y_true, y_pred=y_pred)
5.57999

With masked inputs (useful for ragged inputs):

>>> y_true = {
...     "labels": np.array([[1.0, 0.0, 1.0, 3.0], [0.0, 1.0, 2.0, 3.0]]),
...     "mask": np.array(
...         [[True, True, True, True], [True, True, False, False]]
...     ),
... }
>>> y_pred = np.array([[1.0, 3.0, 2.0, 4.0], [1.0, 1.8, 2.0, 3.0]])
>>> pairwise_mse(y_true=y_true, y_pred=y_pred)
4.76000

With sample_weight:

>>> y_true = np.array([[1.0, 0.0, 1.0, 3.0], [0.0, 1.0, 2.0, 3.0]])
>>> y_pred = np.array([[1.0, 3.0, 2.0, 4.0], [1.0, 1.8, 2.0, 3.0]])
>>> sample_weight = np.array(
...     [[2.0, 3.0, 1.0, 1.0], [2.0, 1.0, 0.0, 0.0]]
... )
>>> pairwise_mse = keras_rs.losses.PairwiseMeanSquaredError()
>>> pairwise_mse(
...     y_true=y_true, y_pred=y_pred, sample_weight=sample_weight
... )
11.0500

Using 'none' reduction:

>>> y_true = np.array([[1.0, 0.0, 1.0, 3.0], [0.0, 1.0, 2.0, 3.0]])
>>> y_pred = np.array([[1.0, 3.0, 2.0, 4.0], [1.0, 1.8, 2.0, 3.0]])
>>> pairwise_mse = keras_rs.losses.PairwiseMeanSquaredError(
...     reduction="none"
... )
>>> pairwise_mse(y_true=y_true, y_pred=y_pred)
[[11., 17.,  5.,  5.], [2.04, 1.3199998, 1.6399999, 1.6399999]]

[source]

call method

PairwiseMeanSquaredError.call(y_true: Any, y_pred: Any)

Compute the pairwise loss.

Arguments

• y_true: tensor or dict. Ground truth values. If tensor, of shape (list_size) for unbatched inputs or (batch_size, list_size) for batched inputs. If an item has a label of -1, it is ignored in loss computation. If it is a dictionary, it should have two keys: "labels" and "mask". "mask" can be used to ignore elements in loss computation, i.e., pairs will not be formed with those items. Note that the final mask is an and of the passed mask, and labels >= 0.
• y_pred: tensor. The predicted values, of shape (list_size) for unbatched inputs or (batch_size, list_size) for batched inputs. Should be of the same shape as y_true.

Returns

The loss.