# tfr.keras.losses.ApproxNDCGLoss

Computes approximate NDCG loss between y_true and y_pred.

Implementation of ApproxNDCG loss (Qin et al, 2008; Bruch et al, 2019). This loss is an approximation for tfr.keras.metrics.NDCGMetric. It replaces the non-differentiable ranking function in NDCG with a differentiable approximation based on the logistic function.

For each list of scores s in y_pred and list of labels y in y_true:

loss = sum_i (2^y_i - 1) / log_2(1 + approxrank(s_i))
approxrank(s_i) = 1 + sum_j (1 / (1 + exp(-(s_j - s_i) / temperature)))


#### Standalone usage:

y_true = [[1., 0.]]
y_pred = [[0.6, 0.8]]
loss = tfr.keras.losses.ApproxNDCGLoss()
loss(y_true, y_pred).numpy()
-0.655107

# Using ragged tensors
y_true = tf.ragged.constant([[1., 0.], [0., 1., 0.]])
y_pred = tf.ragged.constant([[0.6, 0.8], [0.5, 0.8, 0.4]])
loss = tfr.keras.losses.ApproxNDCGLoss(ragged=True)
loss(y_true, y_pred).numpy()
-0.80536866


Usage with the compile() API:

model.compile(optimizer='sgd', loss=tfr.keras.losses.ApproxNDCGLoss())


#### Definition:

$\mathcal{L}(\{y\}, \{s\}) = - \frac{1}{\text{DCG}(y, y)} \sum_{i} \frac{2^{y_i} - 1}{\log_2(1 + \text{rank}_i)}$

where:

$\text{rank}_i = 1 + \sum_{j \neq i} \frac{1}{1 + \exp\left(\frac{-(s_j - s_i)}{\text{temperature} }\right)}$

reduction Type of tf.keras.losses.Reduction to apply to loss. Default value is AUTO. AUTO indicates that the reduction option will be determined by the usage context. For almost all cases this defaults to SUM_OVER_BATCH_SIZE. When used under a tf.distribute.Strategy, except via Model.compile() and Model.fit(), using AUTO or SUM_OVER_BATCH_SIZE will raise an error. Please see this custom training tutorial for more details.
name Optional name for the instance.

## Methods

### from_config

View source

Instantiates a Loss from its config (output of get_config()).

Args
config Output of get_config().

Returns
A Loss instance.

### get_config

View source

Returns the config dictionary for a Loss instance.

### __call__

View source

See tf.keras.losses.Loss.

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