Supplementary Information: Ellipsoidal Multiple Instance Learning
Proof of Lemma 3. We make use of the following mul-tivariate Chebyshev's inequality to proof Lemma 3 sup y∼(¯ y,Σy) Pr[y ∈ S] = 1 1 + d 2 , with d 2 = inf y∈S (y − ¯ y) Σ −1 y (y − ¯ y) (1) Where y is a random vector, the supremum is over all distributions for y with mean ¯ y and covariance matrix Σ y and S is a given convex set.