# Softmax regression bias and prior probabilities for unequal classes

I'm using Softmax regression for a multi-class classification problem. I don't have equal prior probabilities for each of the classes.

I know from Logistic Regression (softmax regression with 2 classes) that the prior probabilities of the classes is implicitly added to the bias ($\log(p_0/p_1)$).

Usually what I do is to manually remove this term from the bias.

My question is, what is the corresponding term in softmax regression bias?

Thanks.

The two facts above imply a maximum is available whenever $\vsigma(\vb)=\vc/n$. This, in turn, suggests a viable initialization for the $i$-th term $b_i$ of the bias $\vb$ is indeed $\log p_i$, the proportion of $i$-labelled examples in the training set (aka the marginal statistics). You might see that you can add any constant to $\vb$ and achieve another likelihood-maximizing bias as well; however, a large scale would get in the way of learning $W$. The relationship with the logistic bias is not coincidental --- this tutorial discusses the similarity.