A Proofs

Consider binary classification and follow our notations, we rewrite the Equation 1 in Kobayashi et al. The last few lines follow from the definition of conditional probabilities. Proposition A.2. Assume that the loss function This claim immediately follows Lemma A.1, where we shows that In this section, we provide results for instance level feedback in the MIL setting. We then train it with a binary cross entropy. We bold the highest value and both if the standard-errors overlap.