Why is the cost function in logistic regression divided by m and not 2m?

Course Q&A Machine Learning Specialization Supervised ML: Regression and Classification
1

In linear regression, I understand that we divide the sum of loss by 2m instead of m to make the derivations mathematically more convenient, but in the cost function of logistic regression, it shows that we only divide the sum of loss by m and not 2m, why is this? Would it not also make later calculations simpler like in linear regression if we used 2m? Thanks

2

In linear regression, the cost function is MSE, which is “Mean Squared Error”. So when you take the derivative of the error squared, you get a factor of 2.

The loss function for Logistic Regression does not involve squaring anything: it involves logarithms, right? So a factor of \frac {1}{2} would not give you any simplification: it would just be extra baggage.

Note that multiplying the loss by a constant does nothing in terms of what solution you end up getting: the same input point that minimizes J will also minimize 2J, right? As you say, it’s just a matter of mathematical convenience by making the formulas simpler.

1 Like