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

  • $\begingroup$ What is the relationship between p(x) and the rho-function. Also what does superscript - mean? Cant find the reference either by googling. $\endgroup$ – Jesper for President Dec 17 '18 at 10:19
  • $\begingroup$ @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. $\endgroup$ – Annalise Azzopardi Dec 17 '18 at 18:36

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