The θ is obtained from the stickbreaking process (Blei and Jordan, 2004), with where β k are independent draws from the beta distribution β(1, α).
in this mechanism, for each y i,j in noisy corpus, it allows 1 → 0 (noisy feature) for features, and allow 1 → 0 (label with no supportive features) or 0 → 1 (incomplete label) for labels.