Add perplexity loss algorithm (#11028)

machine_learning/loss_functions.py

@@ -379,6 +379,98 @@ def mean_absolute_percentage_error(
     return np.mean(absolute_percentage_diff)
 
 
+def perplexity_loss(
+    y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-7
+) -> float:
+    """
+    Calculate the perplexity for the y_true and y_pred.
+
+    Compute the Perplexity which useful in predicting language model
+    accuracy in Natural Language Processing (NLP.)
+    Perplexity is measure of how certain the model in its predictions.
+
+    Perplexity Loss = exp(-1/N (Σ ln(p(x)))
+
+    Reference:
+    https://en.wikipedia.org/wiki/Perplexity
+
+    Args:
+        y_true: Actual label encoded sentences of shape (batch_size, sentence_length)
+        y_pred: Predicted sentences of shape (batch_size, sentence_length, vocab_size)
+        epsilon: Small floating point number to avoid getting inf for log(0)
+
+    Returns:
+        Perplexity loss between y_true and y_pred.
+
+    >>> y_true = np.array([[1, 4], [2, 3]])
+    >>> y_pred = np.array(
+    ...    [[[0.28, 0.19, 0.21 , 0.15, 0.15],
+    ...      [0.24, 0.19, 0.09, 0.18, 0.27]],
+    ...      [[0.03, 0.26, 0.21, 0.18, 0.30],
+    ...       [0.28, 0.10, 0.33, 0.15, 0.12]]]
+    ... )
+    >>> perplexity_loss(y_true, y_pred)
+    5.0247347775367945
+    >>> y_true = np.array([[1, 4], [2, 3]])
+    >>> y_pred = np.array(
+    ...    [[[0.28, 0.19, 0.21 , 0.15, 0.15],
+    ...      [0.24, 0.19, 0.09, 0.18, 0.27],
+    ...      [0.30, 0.10, 0.20, 0.15, 0.25]],
+    ...      [[0.03, 0.26, 0.21, 0.18, 0.30],
+    ...       [0.28, 0.10, 0.33, 0.15, 0.12],
+    ...       [0.30, 0.10, 0.20, 0.15, 0.25]],]
+    ... )
+    >>> perplexity_loss(y_true, y_pred)
+    Traceback (most recent call last):
+    ...
+    ValueError: Sentence length of y_true and y_pred must be equal.
+    >>> y_true = np.array([[1, 4], [2, 11]])
+    >>> y_pred = np.array(
+    ...    [[[0.28, 0.19, 0.21 , 0.15, 0.15],
+    ...      [0.24, 0.19, 0.09, 0.18, 0.27]],
+    ...      [[0.03, 0.26, 0.21, 0.18, 0.30],
+    ...       [0.28, 0.10, 0.33, 0.15, 0.12]]]
+    ... )
+    >>> perplexity_loss(y_true, y_pred)
+    Traceback (most recent call last):
+    ...
+    ValueError: Label value must not be greater than vocabulary size.
+    >>> y_true = np.array([[1, 4]])
+    >>> y_pred = np.array(
+    ...    [[[0.28, 0.19, 0.21 , 0.15, 0.15],
+    ...      [0.24, 0.19, 0.09, 0.18, 0.27]],
+    ...      [[0.03, 0.26, 0.21, 0.18, 0.30],
+    ...       [0.28, 0.10, 0.33, 0.15, 0.12]]]
+    ... )
+    >>> perplexity_loss(y_true, y_pred)
+    Traceback (most recent call last):
+    ...
+    ValueError: Batch size of y_true and y_pred must be equal.
+    """
+
+    vocab_size = y_pred.shape[2]
+
+    if y_true.shape[0] != y_pred.shape[0]:
+        raise ValueError("Batch size of y_true and y_pred must be equal.")
+    if y_true.shape[1] != y_pred.shape[1]:
+        raise ValueError("Sentence length of y_true and y_pred must be equal.")
+    if np.max(y_true) > vocab_size:
+        raise ValueError("Label value must not be greater than vocabulary size.")
+
+    # Matrix to select prediction value only for true class
+    filter_matrix = np.array(
+        [[list(np.eye(vocab_size)[word]) for word in sentence] for sentence in y_true]
+    )
+
+    # Getting the matrix containing prediction for only true class
+    true_class_pred = np.sum(y_pred * filter_matrix, axis=2).clip(epsilon, 1)
+
+    # Calculating perplexity for each sentence
+    perp_losses = np.exp(np.negative(np.mean(np.log(true_class_pred), axis=1)))
+
+    return np.mean(perp_losses)
+
+
 if __name__ == "__main__":
     import doctest