# Discriminative conditional restricted Boltzmann machine for discrete choice and latent variable modelling

## TL;DR

This paper introduces a novel discriminative conditional restricted Boltzmann machine approach for estimating latent variables in discrete choice models without relying on subjective survey questions, using a graphical and machine learning-based framework.

## Contribution

It proposes a new non-parametric, generative modelling method using restricted Boltzmann machines to infer latent behavior factors directly from choice data, bypassing traditional measurement indicators.

## Key findings

- Successfully applied to financial choice data demonstrating latent variable extraction.
- Statistical tests confirm the significance and influence of latent factors on choices.
- Model shows robustness to input variability and sampling.

## Abstract

Conventional methods of estimating latent behaviour generally use attitudinal questions which are subjective and these survey questions may not always be available. We hypothesize that an alternative approach can be used for latent variable estimation through an undirected graphical models. For instance, non-parametric artificial neural networks. In this study, we explore the use of generative non-parametric modelling methods to estimate latent variables from prior choice distribution without the conventional use of measurement indicators. A restricted Boltzmann machine is used to represent latent behaviour factors by analyzing the relationship information between the observed choices and explanatory variables. The algorithm is adapted for latent behaviour analysis in discrete choice scenario and we use a graphical approach to evaluate and understand the semantic meaning from estimated parameter vector values. We illustrate our methodology on a financial instrument choice dataset and perform statistical analysis on parameter sensitivity and stability. Our findings show that through non-parametric statistical tests, we can extract useful latent information on the behaviour of latent constructs through machine learning methods and present strong and significant influence on the choice process. Furthermore, our modelling framework shows robustness in input variability through sampling and validation.