# Binary Loss Function

Currently I am working on Lasso Logistic Regression and in the book by Bulhmann et.al (2011) page 48, it is claimed that the binary loss classification function is given by,

$$\rho(f,y) = log (1+exp(-(-2y-1)f))$$

where $$p(x) = (1+e^-2f)^-1$$

Anyone has managed to solve this because I am not able to solve it, I have tried substituting in

$$y'log(p(x))+(1-y')log(1-p(x)))$$

where $$y'=(y+1)/2$$

• What is the relationship between p(x) and the rho-function. Also what does superscript - mean? Cant find the reference either by googling. – Jesper for President Dec 17 '18 at 10:19
• @JesperHybel the link for the (springer.com/gp/book/9783642201912) for the above mentioned link. So p(x) is the binomial distribution and pho is the loss function for the negative log-likelihood. – Annalise Azzopardi Dec 17 '18 at 18:36