Why are the cost function and mean squared errors called the same thing? WHEN THE COST FUNCTION IS 1/2M AND THE MSE IS 1/N. AND M=N
In completing our friend answer i can say briefly dividing the MSE or some cost functions by 2 is a common practice to simplify mathematical calculations and derivatives, but it does not fundamentally change the interpretation or relative performance of different models.
For example, when you take the derivative of the MSE loss function, dividing it by 2 simplifies the calculations and eliminates the constant term. This can be seen in optimization algorithms like gradient descent, where the derivative of the loss function is used to update the model's parameters.