Social networks serve as important platforms for users to express, exchange and form opinions on various topics. Several opinion dynamics models have been proposed to characterize how a user iteratively updates her expressed opinion based on her innate opinion and the opinion of her neighbors. The extent to how much a user is influenced by her neighboring opinions, as opposed to her own innate opinion, is governed by a measure of her “conformity’ parameter. Characterizing this degree of conformity for users of a social network is critical for several applications such as debiasing online surveys and finding social influencers. In this paper, we address the problem of estimating these conformity values for users, using only the expressed opinions and the social graph. We pose this problem in a constrained optimization framework and design efficient algorithms, which we validate on both synthetic and real-world Twitter data. Using these estimated conformity values, we then address the problem of identifying the smallest subset of users in a social graph that, when seeded initially with some non-neutral opinions, can accurately explain the current opinion values of users in the entire social graph. We call this problem seed recovery. Using ideas from compressed sensing, we analyze and design algorithms for both conformity estimation and seed recovery, and validate them on real and synthetic data.