Active Matrix Factorization for Surveys

Amid historically low response rates, survey researchers seek ways to reduce respondent burden while measuring desired concepts with precision. We propose to ask fewer questions of respondents and impute missing responses via probabilistic matrix factorization. The most informative questions per respondent are chosen sequentially using active learning with variance minimization. We begin with Gaussian responses standard in matrix completion and derive a simple active strategy with closed-form posterior updates. Next we model responses more realistically as ordinal logit; posterior inference and question selection are adapted to the nonconjugate setting. We simulate our matrix sampling procedure on data from real-world surveys. Our active question selection achieves efficiency gains over baselines and can benefit from available side information about respondents.