Active Learning for Non-Parametric Choice Models

TL;DR

This paper introduces an active learning algorithm for non-parametric choice models that uses a DAG representation to improve the estimation of consumer preferences from noisy data, overcoming identifiability issues.

Contribution

It presents a novel DAG-based representation for non-parametric choice models and an inclusion-exclusion method to accurately estimate the DAG from noisy data during active learning.

Findings

Algorithm efficiently estimates the DAG in polynomial time for random frequent sets.

Active learning improves the recovery of frequent preferences over non-active methods.

Method performs well on synthetic and real consumer preference datasets.

Abstract

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.