# Bayesian Automatic Relevance Determination for Utility Function Specification in Discrete Choice Models

## TL;DR

This paper introduces a Bayesian method with automatic relevance determination to efficiently identify optimal utility functions in discrete choice models, improving accuracy and scalability for large datasets.

## Contribution

It develops a scalable Bayesian framework with variational inference for automatic utility function specification in discrete choice models, handling high-dimensional data.

## Key findings

- Accurately recovers true utility functions in semi-artificial data
- Discovers high-quality utility specifications in real data
- Outperforms previous methods on multiple criteria

## Abstract

Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This paper seeks to help modellers by leveraging the Bayesian framework and the concept of automatic relevance determination (ARD), in order to automatically determine an optimal utility function specification from an exponentially large set of possible specifications in a purely data-driven manner. Based on recent advances in approximate Bayesian inference, a doubly stochastic variational inference is developed, which allows the proposed DCM-ARD model to scale to very large and high-dimensional datasets. Using semi-artificial choice data, the proposed approach is shown to very accurately recover the true utility function specifications that govern the observed choices. Moreover, when applied to real choice data, DCM-ARD is shown to be able discover high quality specifications that can outperform previous ones from the literature according to multiple criteria, thereby demonstrating its practical applicability.