Observation-wise logloss / crossentropy

[jemus42]

In the context of #39, I would have use for the instance-wise logloss as e.g. available in Metrics::ll.

I cloned the repo to see if I can prepare this myself, but then I got sidetracked thinking about logloss as it is implemented right now, which from what I gather works for both binary and multiclass tasks. In the instance-wise case however it would need to be split into basically blogloss and mlogloss, akin to bbrier and mbrier, no?

So I'm not sure how to go about all that.

I would assume we'd have something along these lines if I understand correctly, yes?

blogloss_obs = function(truth, prob, positive, eps = 1e-15, ...) {
  assert_binary(truth, prob = prob, positive = positive)
  assert_number(eps, lower = 0, upper = 1)
  
  ii = match(as.character(truth), colnames(prob))
  p = prob[cbind(seq_len(nrow(prob)), ii)]
  p = pmax(eps, pmin(1 - eps, p))
  truth = as.integer(truth == positive)
  -(truth * log(p) + (1 - truth) * log(1 - p))
}

mlogloss_obs = function(truth, prob, eps = 1e-15, ...) {
  assert_classif(truth, prob = prob)
  assert_number(eps, lower = 0, upper = 1)

  ii = match(as.character(truth), colnames(prob))
  p = prob[cbind(seq_len(nrow(prob)), ii)]
  p = pmax(eps, pmin(1 - eps, p))
  log(p)
}