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86 lines
2.8 KiB
Python
86 lines
2.8 KiB
Python
"""
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Categorical Cross-Entropy Loss
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This function calculates the Categorical Cross-Entropy Loss between true class
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labels and predicted class probabilities.
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Formula:
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Categorical Cross-Entropy Loss = -Σ(y_true * ln(y_pred))
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Resources:
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- [Wikipedia - Cross entropy](https://en.wikipedia.org/wiki/Cross_entropy)
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"""
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import numpy as np
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def categorical_cross_entropy(
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y_true: np.ndarray, y_pred: np.ndarray, epsilon: float = 1e-15
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) -> float:
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"""
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Calculate Categorical Cross-Entropy Loss between true class labels and
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predicted class probabilities.
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Parameters:
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- y_true: True class labels (one-hot encoded) as a NumPy array.
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- y_pred: Predicted class probabilities as a NumPy array.
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- epsilon: Small constant to avoid numerical instability.
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Returns:
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- ce_loss: Categorical Cross-Entropy Loss as a floating-point number.
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Example:
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>>> true_labels = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
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>>> pred_probs = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1], [0.0, 0.1, 0.9]])
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>>> categorical_cross_entropy(true_labels, pred_probs)
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0.567395975254385
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>>> y_true = np.array([[1, 0], [0, 1]])
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>>> y_pred = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
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>>> categorical_cross_entropy(y_true, y_pred)
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Traceback (most recent call last):
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...
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ValueError: Input arrays must have the same shape.
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>>> y_true = np.array([[2, 0, 1], [1, 0, 0]])
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>>> y_pred = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
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>>> categorical_cross_entropy(y_true, y_pred)
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Traceback (most recent call last):
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...
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ValueError: y_true must be one-hot encoded.
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>>> y_true = np.array([[1, 0, 1], [1, 0, 0]])
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>>> y_pred = np.array([[0.9, 0.1, 0.0], [0.2, 0.7, 0.1]])
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>>> categorical_cross_entropy(y_true, y_pred)
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Traceback (most recent call last):
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...
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ValueError: y_true must be one-hot encoded.
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>>> y_true = np.array([[1, 0, 0], [0, 1, 0]])
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>>> y_pred = np.array([[0.9, 0.1, 0.1], [0.2, 0.7, 0.1]])
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>>> categorical_cross_entropy(y_true, y_pred)
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Traceback (most recent call last):
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...
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ValueError: Predicted probabilities must sum to approximately 1.
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"""
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if y_true.shape != y_pred.shape:
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raise ValueError("Input arrays must have the same shape.")
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if np.any((y_true != 0) & (y_true != 1)) or np.any(y_true.sum(axis=1) != 1):
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raise ValueError("y_true must be one-hot encoded.")
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if not np.all(np.isclose(np.sum(y_pred, axis=1), 1, rtol=epsilon, atol=epsilon)):
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raise ValueError("Predicted probabilities must sum to approximately 1.")
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# Clip predicted probabilities to avoid log(0)
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y_pred = np.clip(y_pred, epsilon, 1)
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# Calculate categorical cross-entropy loss
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return -np.sum(y_true * np.log(y_pred))
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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