Extreme Multi - label Loss Functions for Recommendation , Tagging , Ranking & Other Missing Label Applications – Supplementary Material
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چکیده
1. PROPENSITY SCORED LOSSES This section provides proofs for all the theorems stated in Section 4 of the paper. Theorem 4.1. The loss function L(y, ŷ) evaluated on the observed ground truth y is an unbiased estimator of the true loss function L∗(y∗, ŷ) evaluated on complete ground truth y∗. Thus, Ey[L(y, ŷ)] = Ey∗ [L∗(y∗, ŷ)], for any P (y∗) and P (y) related through propensities pl and any fixed ŷ. Proof. Ey[L(y, ŷ)] = ∑
منابع مشابه
Extreme Multi - label Loss Functions for Recommendation , Tagging , Ranking & Other Missing Label Applications – Supplementary
1. PROPENSITY SCORED LOSSES Theorem 4.1. The loss function L(y, ˆ y) evaluated on the observed ground truth y is an unbiased estimator of the true loss function L * (y * , ˆ y) evaluated on complete ground truth y *. Thus, Ey[L(y, ˆ y)] = Ey * [L * (y * , ˆ y)], for any P (y *) and P (y) related through propensities p l and any fixedˆy. Proof.
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