Created folder for losses in Machine_Learning (TheAlgorithms#9969)

* Created folder for losses in Machine_Learning

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Co-authored-by: Christian Clauss <[email protected]>

* Update machine_learning/losses/mean_squared_error.py

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* Update machine_learning/losses/binary_cross_entropy.py

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* Update mean_squared_error.py

* Update machine_learning/losses/mean_squared_error.py

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* Update binary_cross_entropy.py

* Update mean_squared_error.py

* Update binary_cross_entropy.py

* Update mean_squared_error.py

* Update mean_squared_error.py

* Update binary_cross_entropy.py

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>
Co-authored-by: Tianyi Zheng <[email protected]>

Author: 4 people

Diff for: machine_learning/loss_functions/binary_cross_entropy.py

@@ -0,0 +1,59 @@
+"""
+Binary Cross-Entropy (BCE) Loss Function
+
+Description:
+Quantifies dissimilarity between true labels (0 or 1) and predicted probabilities.
+It's widely used in binary classification tasks.
+
+Formula:
+BCE = -Σ(y_true * log(y_pred) + (1 - y_true) * log(1 - y_pred))
+
+Source:
+[Wikipedia - Cross entropy](https://en.wikipedia.org/wiki/Cross_entropy)
+"""
+
+import numpy as np
+
+
+def binary_cross_entropy(
+    y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-15
+) -> float:
+    """
+    Calculate the BCE Loss between true labels and predicted probabilities.
+
+    Parameters:
+    - y_true: True binary labels (0 or 1).
+    - y_pred: Predicted probabilities for class 1.
+    - epsilon: Small constant to avoid numerical instability.
+
+    Returns:
+    - bce_loss: Binary Cross-Entropy Loss.
+
+    Example Usage:
+    >>> 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.")
+    # Clip predicted probabilities to avoid log(0) and log(1)
+    y_pred = np.clip(y_pred, epsilon, 1 - epsilon)
+
+    # Calculate binary cross-entropy loss
+    bce_loss = -(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))
+
+    # Take the mean over all samples
+    return np.mean(bce_loss)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

Diff for: machine_learning/loss_functions/mean_squared_error.py

@@ -0,0 +1,51 @@
+"""
+Mean Squared Error (MSE) Loss Function
+
+Description:
+MSE measures the mean squared difference between true values and predicted values.
+It serves as a measure of the model's accuracy in regression tasks.
+
+Formula:
+MSE = (1/n) * Σ(y_true - y_pred)^2
+
+Source:
+[Wikipedia - Mean squared error](https://en.wikipedia.org/wiki/Mean_squared_error)
+"""
+
+import numpy as np
+
+
+def mean_squared_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculate the Mean Squared Error (MSE) between two arrays.
+
+    Parameters:
+    - y_true: The true values (ground truth).
+    - y_pred: The predicted values.
+
+    Returns:
+    - mse: The Mean Squared Error between y_true and y_pred.
+
+    Example usage:
+    >>> 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_error(true_values, predicted_values)
+    0.028000000000000032
+    >>> 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)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()