Businesses seek to use "big data" to learn consumer preferences, but they need to overcome data challenges that are economic, societal, and computational. Use fewer customers to learn faster, use less data from any one consumer, and be robust to their inconsistent responses. The goal of our cube is to learn preferences from data with limited feedback and as few requests of the user as possible. We consider two kinds of feedback from consumers: binary feedback (clicks) and comparative feedback (ranking). Such choice tasks are central to the marketing research method conjoint analysis. Researchers in marketing and machine learning have sought to develop optimal and efficient algorithms in terms of both number of queries and computational complexity. We will investigate non-convex machine learning formulations with efficient implementations and marketing approaches for efficient queries, such as maximum-difference surveys, extended to adaptive and sequential responses.