Two spam filters are tested on the same four emails. Each filter outputs the probability that an email is spam.
| truly spam? | Filter A's spam probability | Filter B's spam probability | |
|---|---|---|---|
| 1 | yes | ||
| 2 | no | ||
| 3 | no | ||
| 4 | no |
With a cut-off, both filters label emails 1–3 correctly and email 4 wrongly, so both are accurate.
Each is scored with cross-entropy: the loss on one email is , where is the probability the filter gave to that email's true label, and a filter's loss is the average over the four emails.
What is each filter's loss, to 2 decimal places, and which is lower?
Select all that apply.