How is bayesian risk computed to prune decision trees?
I'm going to try to answer my question. To (4), I would say yes. For (5), I believe that for each node, there's a specific partition that falls into the node when following the branches down the decision tree. For instance, for Node 2, there are 3 instances (where a=1) that results in [Yes, No, No] for the partitioned output class at Node 2. For (1), I would calculate the risks over each of these relevant examples and sum them. Then at node 2: $\frac{2}{3}(1)+\frac{1}{3}(1)+\frac{1}{3}(1) = \frac{4}{3}$ is the bayes risk where I use 0-1 loss. Then I would use these estimated risks in the pruning algorithm. Can anyone corroborate?
(2) was answered in the comments above, and I'm assuming for (3) that cross-entropy can be used for multi-class loss.