Based on Theorem 1, under the conditional independence assumption, Corr(P (Y = 1|X), P (C = 1|X)) 2 equals 1, so that Corr(P (Y = 1|X), P (Y = 1|P (C = 1|X))) 2 equals 1 as well.
in the following sections, when we aim to investigate the impact of a single context feature C k or a single task Y t , for simplicity, we use a random variable C or Y to denote C k or Y t respectively.