Early Gains Matter: A Case for Preferring Generative over Discriminative Crowdsourcing Models

Introduction. Here we derive mean field variational updates for MOMRESP. Although this derivation is largely a mechanical exercise, it is our belief that there is a contingent of crowdsourcing practitioners whose background is more practical than theoretical and who may appreciate seeing the mechanics of mean-field variational inference presented in a high level of detail for a model they are familiar with. The updates for LOGRESP involve so much overlap with those for MOMRESP that we leave them as an exercise for the interested reader. Problem Setup. Given some posterior distribution p∗ over variables z, our goal is to search among some family of simpler approximate tractable models Q and identify the q(z) ∈ Q that most closely resembles p∗(z). If we choose Q to be the set of fully factored models such that q(z) = ∏qi(zi) (the mean-field assumption) then the q that minimizes KL divergence KL(q||p∗) can be shown to have the following form: