We study the problem of actively learning a non-parametric choice model based on consumers' decisions. We present a negative result showing that such choice models may not be identifiable. To overcome the identifiability problem, we introduce a directed acyclic graph (DAG) representation of the choice model. This representation provably encodes all the information about the choice model which can be inferred from the available data, in the sense that it permits computing all choice probabilities.
We establish that given exact choice probabilities for a collection of item sets, one can reconstruct the DAG. However, attempting to extend this methodology to estimate the DAG from noisy choice frequency data obtained during an active learning process leads to inaccuracies. To address this challenge, we present an inclusion-exclusion approach that effectively manages error propagation across DAG levels, leading to a more accurate estimate of the DAG. Utilizing this technique, our algorithm estimates the DAG representation of an underlying non-parametric choice model. The algorithm operates efficiently (in polynomial time) when the set of frequent rankings is drawn uniformly at random. It learns the distribution over the most popular items among frequent preference types by actively and repeatedly offering assortments of items and observing the chosen item. We demonstrate that our algorithm more effectively recovers a set of frequent preferences on both synthetic and publicly available datasets on consumers' preferences, compared to corresponding non-active learning estimation algorithms. These findings underscore the value of our algorithm and the broader applicability of active-learning approaches in modeling consumer behavior.
Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference
Department of Mathematics, Brigham Young University（数学系， Brigham Young University）；Centre for Mathematical Sciences, Lund University（数学科学中心， Lund University）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（计算工程与科学研究院， The University of Texas at Austin）
On Pareto Optimality for Parametric Choice Bandits
Department of Management Science and Engineering, Tsinghua University, Beijing, China（清华大学管理科学与工程系，北京，中国）；Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore（新加坡国立大学工业系统工程与管理系，新加坡）
Incorporating uncertainty quantification into travel mode choice modeling: a Bayesian neural network (BNN) approach and an uncertainty-guided active survey framework
