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Preference Measurement (PM) has a long history in marketing, healthcare, and the bio-behavioral sciences, where conjoint analysis is commonly used. The goal of PM is to learn the utility function of an individual or a group of individuals from expressed preference data (buying patterns, surveys, ratings), possibly contaminated with outliers. For metric conjoint data, a robust part worth estimator is developed on the basis of a neat connection between (pseudo)norm-regularized regression, and the least-trimmed squared estimator. This connection suggests efficient solvers based on convex relaxation, which leads naturally to a family of robust estimators subsuming Huber optimal M-class.
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