# “Return values” of univariate logistic regression

I read an interesting article on an approach to calibrate probabilistic classifiers (Kull et al. 2017, "Beyond sigmoids: How to obtain well-calibrated probabilities from binary classifiers with beta calibration") and stumbled across a formulation that is unclear to me.

In the second step of algorithm 1 the authors write

$$(a,c) \leftarrow \mathrm{fit\: univariate\: logistic \:regression \: to \: predict \: y_{train}\: from\: \mathbf{s}'}$$

which left me confused. In my understanding this assigns the "return values" of the logistic regression fit to the variables $$a$$ and $$c$$. While the authors state that this approach to acquire these two parameters for their function makes it possible to use any implementation of logistic regression, these usually only either return a model object or the coefficients of the model (which should amount to the same).

On page 8, section 3.1, the authors introduce the parameters $$a,b,c$$ and in proposition 1 they show that the likelihood ratio of the logistic model is equal to that of their parameterization of the used beta distribution, which is supposed to show that fitting a logistic model to acquire the parameters is sufficient - however they don't seem to write a word about the formulation above besides

Hence, we can use logistic calibration (i.e. univariate logistic regression) to fit the beta[a=b] calibration maps, as shown in Algorithm 1.

Maybe this is just too trivial for the authors to write more explicitly, can someone explain to me what exactly the authors assign to $$a$$ and $$c$$ here?

• Did you answer this on your own or you want help? I read the paper but I did not invest the time to write an answer. (I like your questions in general, very thoughtful +1.) – usεr11852 Apr 3 at 22:27
• No i did not answer it, I had to move my attention elsewhere. Id still appreciate an answer, if its not too much to ask ;) – deemel Apr 4 at 5:30
• I have not forgot about this. I just try to reproduce the results from the paper but I do not get the time! (I have seen the repo.) – usεr11852 Apr 11 at 0:02
• No sweat, I don't need this for work anymore, I'm merely curious ;) – deemel Apr 11 at 4:53