I have a dataset where I don't have the exact output labels $y$ but what I have is if $y$ is larger or smaller than another value $z.$ There is another binary parameter $b $ that decides if y is larger or smaller than $z.$ If $b=0,~ y$ is smaller than $z$ and if $b=1,~ y$ is larger than $z.$ I want to develop a regression model for this. more specifically I want to find the log-likelihood for the observed data which is a triple of $(x,z,b).$ How do I go about solving this problem?



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