Added Mean Squared Logarithmic Error (MSLE) Loss Function (#10637)

* Added Mean Squared Logarithmic Error (MSLE)

* Added Mean Squared Logarithmic Error (MSLE)

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: ank426

machine_learning/loss_functions/mean_squared_logarithmic_error.py

@@ -0,0 +1,55 @@
+"""
+Mean Squared Logarithmic Error (MSLE) Loss Function
+
+Description:
+MSLE measures the mean squared logarithmic difference between
+true values and predicted values, particularly useful when
+dealing with regression problems involving skewed or large-value
+targets. It is often used when the relative differences between
+predicted and true values are more important than absolute
+differences.
+
+Formula:
+MSLE = (1/n) * Σ(log(1 + y_true) - log(1 + y_pred))^2
+
+Source:
+(https://insideaiml.com/blog/MeanSquared-Logarithmic-Error-Loss-1035)
+"""
+
+import numpy as np
+
+
+def mean_squared_logarithmic_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculate the Mean Squared Logarithmic Error (MSLE) between two arrays.
+
+    Parameters:
+    - y_true: The true values (ground truth).
+    - y_pred: The predicted values.
+
+    Returns:
+    - msle: The Mean Squared Logarithmic 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_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()