Consolidate loss functions into a single file (TheAlgorithms#10737)

* Consolidate loss functions into single file

* updating DIRECTORY.md

* Fix typo

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: tianyizheng02

Diff for: DIRECTORY.md

@@ -549,13 +549,7 @@
   * Local Weighted Learning
     * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py)
   * [Logistic Regression](machine_learning/logistic_regression.py)
-  * Loss Functions
-    * [Binary Cross Entropy](machine_learning/loss_functions/binary_cross_entropy.py)
-    * [Categorical Cross Entropy](machine_learning/loss_functions/categorical_cross_entropy.py)
-    * [Hinge Loss](machine_learning/loss_functions/hinge_loss.py)
-    * [Huber Loss](machine_learning/loss_functions/huber_loss.py)
-    * [Mean Squared Error](machine_learning/loss_functions/mean_squared_error.py)
-    * [Mean Squared Logarithmic Error](machine_learning/loss_functions/mean_squared_logarithmic_error.py)
+  * [Loss Functions](machine_learning/loss_functions.py)
   * [Mfcc](machine_learning/mfcc.py)
   * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py)
   * [Polynomial Regression](machine_learning/polynomial_regression.py)

Diff for: machine_learning/loss_functions.py

@@ -0,0 +1,252 @@
+import numpy as np
+
+
+def binary_cross_entropy(
+    y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-15
+) -> float:
+    """
+    Calculate the mean binary cross-entropy (BCE) loss between true labels and predicted
+    probabilities.
+
+    BCE loss quantifies dissimilarity between true labels (0 or 1) and predicted
+    probabilities. It's widely used in binary classification tasks.
+
+    BCE = -Σ(y_true * ln(y_pred) + (1 - y_true) * ln(1 - y_pred))
+
+    Reference: https://en.wikipedia.org/wiki/Cross_entropy
+
+    Parameters:
+    - y_true: True binary labels (0 or 1)
+    - y_pred: Predicted probabilities for class 1
+    - epsilon: Small constant to avoid numerical instability
+
+    >>> true_labels = np.array([0, 1, 1, 0, 1])
+    >>> predicted_probs = np.array([0.2, 0.7, 0.9, 0.3, 0.8])
+    >>> binary_cross_entropy(true_labels, predicted_probs)
+    0.2529995012327421
+    >>> true_labels = np.array([0, 1, 1, 0, 1])
+    >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
+    >>> binary_cross_entropy(true_labels, predicted_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Input arrays must have the same length.")
+
+    y_pred = np.clip(y_pred, epsilon, 1 - epsilon)  # Clip predictions to avoid log(0)
+    bce_loss = -(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))
+    return np.mean(bce_loss)
+
+
+def categorical_cross_entropy(
+    y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-15
+) -> float:
+    """
+    Calculate categorical cross-entropy (CCE) loss between true class labels and
+    predicted class probabilities.
+
+    CCE = -Σ(y_true * ln(y_pred))
+
+    Reference: https://en.wikipedia.org/wiki/Cross_entropy
+
+    Parameters:
+    - y_true: True class labels (one-hot encoded)
+    - y_pred: Predicted class probabilities
+    - epsilon: Small constant to avoid numerical instability
+
+    >>> true_labels = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1], [0.0, 0.1, 0.9]])
+    >>> categorical_cross_entropy(true_labels, pred_probs)
+    0.567395975254385
+    >>> true_labels = np.array([[1, 0], [0, 1]])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
+    >>> categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input arrays must have the same shape.
+    >>> true_labels = np.array([[2, 0, 1], [1, 0, 0]])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
+    >>> categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: y_true must be one-hot encoded.
+    >>> true_labels = np.array([[1, 0, 1], [1, 0, 0]])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
+    >>> categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: y_true must be one-hot encoded.
+    >>> true_labels = np.array([[1, 0, 0], [0, 1, 0]])
+    >>> pred_probs = np.array([[0.9, 0.1, 0.1], [0.2, 0.7, 0.1]])
+    >>> categorical_cross_entropy(true_labels, pred_probs)
+    Traceback (most recent call last):
+        ...
+    ValueError: Predicted probabilities must sum to approximately 1.
+    """
+    if y_true.shape != y_pred.shape:
+        raise ValueError("Input arrays must have the same shape.")
+
+    if np.any((y_true != 0) & (y_true != 1)) or np.any(y_true.sum(axis=1) != 1):
+        raise ValueError("y_true must be one-hot encoded.")
+
+    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)
+    return -np.sum(y_true * np.log(y_pred))
+
+
+def hinge_loss(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculate the mean hinge loss for between true labels and predicted probabilities
+    for training support vector machines (SVMs).
+
+    Hinge loss = max(0, 1 - true * pred)
+
+    Reference: https://en.wikipedia.org/wiki/Hinge_loss
+
+    Args:
+    - y_true: actual values (ground truth) encoded as -1 or 1
+    - y_pred: predicted values
+
+    >>> true_labels = np.array([-1, 1, 1, -1, 1])
+    >>> pred = np.array([-4, -0.3, 0.7, 5, 10])
+    >>> hinge_loss(true_labels, pred)
+    1.52
+    >>> true_labels = np.array([-1, 1, 1, -1, 1, 1])
+    >>> pred = np.array([-4, -0.3, 0.7, 5, 10])
+    >>> hinge_loss(true_labels, pred)
+    Traceback (most recent call last):
+    ...
+    ValueError: Length of predicted and actual array must be same.
+    >>> true_labels = np.array([-1, 1, 10, -1, 1])
+    >>> pred = np.array([-4, -0.3, 0.7, 5, 10])
+    >>> hinge_loss(true_labels, pred)
+    Traceback (most recent call last):
+    ...
+    ValueError: y_true can have values -1 or 1 only.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Length of predicted and actual array must be same.")
+
+    if np.any((y_true != -1) & (y_true != 1)):
+        raise ValueError("y_true can have values -1 or 1 only.")
+
+    hinge_losses = np.maximum(0, 1.0 - (y_true * y_pred))
+    return np.mean(hinge_losses)
+
+
+def huber_loss(y_true: np.ndarray, y_pred: np.ndarray, delta: float) -> float:
+    """
+    Calculate the mean Huber loss between the given ground truth and predicted values.
+
+    The Huber loss describes the penalty incurred by an estimation procedure, and it
+    serves as a measure of accuracy for regression models.
+
+    Huber loss =
+        0.5 * (y_true - y_pred)^2                   if |y_true - y_pred| <= delta
+        delta * |y_true - y_pred| - 0.5 * delta^2   otherwise
+
+    Reference: https://en.wikipedia.org/wiki/Huber_loss
+
+    Parameters:
+    - y_true: The true values (ground truth)
+    - y_pred: The predicted values
+
+    >>> true_values = np.array([0.9, 10.0, 2.0, 1.0, 5.2])
+    >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
+    >>> np.isclose(huber_loss(true_values, predicted_values, 1.0), 2.102)
+    True
+    >>> true_labels = np.array([11.0, 21.0, 3.32, 4.0, 5.0])
+    >>> predicted_probs = np.array([8.3, 20.8, 2.9, 11.2, 5.0])
+    >>> np.isclose(huber_loss(true_labels, predicted_probs, 1.0), 1.80164)
+    True
+    >>> true_labels = np.array([11.0, 21.0, 3.32, 4.0])
+    >>> predicted_probs = np.array([8.3, 20.8, 2.9, 11.2, 5.0])
+    >>> huber_loss(true_labels, predicted_probs, 1.0)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Input arrays must have the same length.")
+
+    huber_mse = 0.5 * (y_true - y_pred) ** 2
+    huber_mae = delta * (np.abs(y_true - y_pred) - 0.5 * delta)
+    return np.where(np.abs(y_true - y_pred) <= delta, huber_mse, huber_mae).mean()
+
+
+def mean_squared_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculate the mean squared error (MSE) between ground truth and predicted values.
+
+    MSE measures the squared difference between true values and predicted values, and it
+    serves as a measure of accuracy for regression models.
+
+    MSE = (1/n) * Σ(y_true - y_pred)^2
+
+    Reference: https://en.wikipedia.org/wiki/Mean_squared_error
+
+    Parameters:
+    - y_true: The true values (ground truth)
+    - y_pred: The predicted values
+
+    >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
+    >>> np.isclose(mean_squared_error(true_values, predicted_values), 0.028)
+    True
+    >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
+    >>> mean_squared_error(true_labels, predicted_probs)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Input arrays must have the same length.")
+
+    squared_errors = (y_true - y_pred) ** 2
+    return np.mean(squared_errors)
+
+
+def mean_squared_logarithmic_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculate the mean squared logarithmic error (MSLE) between ground truth and
+    predicted values.
+
+    MSLE measures the squared logarithmic difference between true values and predicted
+    values for regression models. It's particularly useful for dealing with skewed or
+    large-value data, and it's often used when the relative differences between
+    predicted and true values are more important than absolute differences.
+
+    MSLE = (1/n) * Σ(log(1 + y_true) - log(1 + y_pred))^2
+
+    Reference: https://insideaiml.com/blog/MeanSquared-Logarithmic-Error-Loss-1035
+
+    Parameters:
+    - y_true: The true values (ground truth)
+    - y_pred: The predicted values
+
+    >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
+    >>> mean_squared_logarithmic_error(true_values, predicted_values)
+    0.0030860877925181344
+    >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_probs = np.array([0.3, 0.8, 0.9, 0.2])
+    >>> mean_squared_logarithmic_error(true_labels, predicted_probs)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Input arrays must have the same length.")
+
+    squared_logarithmic_errors = (np.log1p(y_true) - np.log1p(y_pred)) ** 2
+    return np.mean(squared_logarithmic_errors)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()