A new statistical model for choice-based conjoint analysis is proposed. The model uses auxiliary variables to account for outliers and to detect the salient features that influence decisions. Unlike recent classification-based approaches to choice-based conjoint analysis, a sparsity-aware maximum likelihood (ML) formulation is proposed to estimate the model parameters. The proposed approach is conceptually appealing, mathematically tractable, and is also well-suited for distributed implementation. Its performance is tested and compared to the prior state-of-art using synthetic as well as real data coming from a conjoint choice experiment for coffee makers, with very promising results.