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Mean Squared Error Derivative

Functions

mean_squared_error_derivative(Y, Y_hat)

Calculate the derivative of the mean squared error loss.

Parameters:

Name Type Description Default
Y ndarray

True values.

 required
Y_hat ndarray

Predicted values.

 required

Returns:

Type Description

numpy.ndarray: The gradient of the mean squared error.
Example 
Y = np.array([[1, 2], [3, 4]])
Y_hat = np.array([[1.1, 2.1], [2.9, 4.1]])
gradient = mean_squared_error_derivative(Y, Y_hat)
print(gradient)
Note

The result is divided by the number of samples (Y.shape[1]) to get the average gradient across all samples.

Source code in microkeras/losses/mean_squared_error_derivative.py 
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def mean_squared_error_derivative(Y, Y_hat):
    """
    Calculate the derivative of the mean squared error loss.

    Args:
        Y (numpy.ndarray): True values.
        Y_hat (numpy.ndarray): Predicted values.

    Returns:
        numpy.ndarray: The gradient of the mean squared error.

    Example:
        ```python
        Y = np.array([[1, 2], [3, 4]])
        Y_hat = np.array([[1.1, 2.1], [2.9, 4.1]])
        gradient = mean_squared_error_derivative(Y, Y_hat)
        print(gradient)
        ```

    Note:
        The result is divided by the number of samples (Y.shape[1])
        to get the average gradient across all samples.
    """
    return 2 * (Y_hat - Y) / Y.shape[1]