Active Learning for NonParametric Choice Models
Abstract
We study the problem of actively learning a nonparametric 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, which in a sense captures as much information about the choice model as could informationtheoretically be identified. We then consider the problem of learning an approximation to this DAG representation in an activelearning setting. We design an efficient activelearning algorithm to estimate the DAG representation of the nonparametric choice model, which runs in polynomial time when the set of frequent rankings is drawn uniformly at random. Our algorithm learns the distribution over the most popular items of frequent preferences by actively and repeatedly offering assortments of items and observing the item chosen. We show that our algorithm can better recover a set of frequent preferences on both a synthetic and publicly available dataset on consumers' preferences, compared to the corresponding nonactive learning estimation algorithms. This demonstrates the value of our algorithm and activelearning approaches more generally.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.03346
 arXiv:
 arXiv:2208.03346
 Bibcode:
 2022arXiv220803346S
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Optimization and Control;
 Mathematics  Probability;
 Statistics  Machine Learning
 EPrint:
 51 pages, 3 figures