Add the sparse categorical cross-entropy loss

machine_learning/loss_functions.py

@@ -148,6 +148,58 @@ def categorical_cross_entropy(
     return -np.sum(y_true * np.log(y_pred))
 
 
+def sparse_categorical_cross_entropy(
+    y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-15
+) -> float:
+    """
+    Calculate sparse categorical cross entropy (SCCE) loss between true class labels and
+    predicted class probabilities. SCCE is used in cases where the true class labels are
+    represented in a sparse matrix format.
+
+    SCCE = -Σ(ln(y_pred[i, y_true[i]]))
+
+    Reference: https://en.wikipedia.org/wiki/Cross_entropy
+
+    Parameters:
+    - y_true: True class labels containing class indices.
+    - y_pred: Predicted class probabilities.
+    - epsilon: Small constant to avoid numerical instability.
+
+    >>> true_labels = np.array([0, 1, 2])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1], [0.0, 0.1, 0.9]])
+    >>> sparse_categorical_cross_entropy(true_labels, pred_probs)
+    0.567395975254385
+
+    >>> true_labels = np.array([1, 2])
+    >>> pred_probs = np.array([[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
+    >>> sparse_categorical_cross_entropy(true_labels, pred_probs)
+    2.353878387381596
+
+    >>> true_labels = np.array([1, 5])
+    >>> pred_probs = np.array([[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
+    >>> sparse_categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: Class labels in y_true are out of range.
+
+    >>> true_labels = np.array([1, 2])
+    >>> pred_probs = np.array([[0.05, 0.95, 0.1], [0.1, 0.8, 0.1]])
+    >>> sparse_categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: Predicted probabilities must sum to approximately 1.
+    """
+    if np.any(y_true >= y_pred.shape[1]) or np.any(y_true < 0):
+        raise ValueError("Class labels in y_true are out of range.")
+
+    if not np.all(np.isclose(np.sum(y_pred, axis=1), 1, rtol=epsilon, atol=epsilon)):
+        raise ValueError("Predicted probabilities must sum to approximately 1.")
+
+    y_pred = np.clip(y_pred, epsilon, 1)  # Clip predictions to avoid log(0)
+    log_preds = np.log(y_pred[np.arange(len(y_pred)), y_true])
+    return -np.sum(log_preds)
+
+
 def categorical_focal_cross_entropy(
     y_true: np.ndarray,
     y_pred: np.ndarray,