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?

In case of a 0-1 coded binary outcome, squared error loss on predicted probabilities (a.k.a. Brier score) is most similar to $\mathrm{VAR}_\mathrm{err}$. The variance of a single-trial binomial variable seems most similar to $\mathrm{VAR}_{\mathrm{tot}}$.
Then
$1 - R^2 = \frac{\mathrm{VAR}_{\mathrm{err}}}{\mathrm{VAR}_{\mathrm{tot}}} = \frac{\frac{1}{n}\sum_i (\hat{p}_i - y_i)^2}{\bar{y} (1-\bar{y})}$
where $n$ is the number of observations the measure of fit was computed on, $\hat{p}_i$ is the model-predicted probability of being in class 1 (versus 0) for observation $i$ and $\bar{y}$ is the baserate, or proportion of observations in class 1.
The $R^2$ thus computed is referred to as Efron’s pseudo R-squared. Wikipedia provides some alternative measures, that are not computed based on squared error loss, but on binomial deviance, for example.
