variance unexplained for binary classifier I found in Wikipedia the definition of fraction of variance unexplained in the case of a regressor. Is there a meaningful definition of variance unexplained for a classifier?

That Wikipedia article is only correct in the case of OLS linear regression. If you estimate the parameters of a linear model another way, such as with regularization, or if you have a nonlinear regression, that interpretation of $R^2$ breaks down.
Interestingly, if you use a linear probability model that you fit via OLS, $R^2$ has the usual interpretation. Linear probability models have their issues, but they do exist, and people do use them in “classification” problems.
In general, however, nonlinear regression models like logistic regressions and neural networks lack the usual interpretation of $R^2$ as the fraction or proportion of variance explained.
