# Combining Discrete Choice Models and Neural Networks through Embeddings: Formulation, Interpretability and Performance

arXiv: https://arxiv.org/abs/2109.12042 · HTML: https://mlsanity.com/paper/2109.12042/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [From Word to Sense Embeddings: A Survey on Vector Representations of Meaning](https://mlsanity.com/paper/1805.04032/) (2018)
- [Urban2Vec: Incorporating Street View Imagery and POIs for Multi-Modal Urban Neighborhood Embedding](https://mlsanity.com/paper/2001.11101/) (2020)
- [Evaluation of sentence embeddings in downstream and linguistic probing tasks](https://mlsanity.com/paper/1806.06259/) (2018)
- [Artificial Neural Networks Applied to Taxi Destination Prediction](https://mlsanity.com/paper/1508.00021/) (2015)
- [Rethinking travel behavior modeling representations through embeddings](https://mlsanity.com/paper/1909.00154/) (2019)

## Built on by (most cited first, 10 of 10)

- [Deep hybrid model with satellite imagery: how to combine demand modeling and computer vision for behavior analysis?](https://mlsanity.com/paper/2303.04204/) (2023)
- [Aligning LLM with human travel choices: a persona-based embedding learning approach](https://mlsanity.com/paper/2505.19003/) (2025)
- [Transformer Choice Net: A Transformer Neural Network for Choice Prediction](https://mlsanity.com/paper/2310.08716/) (2023)
- [A Neural Network Based Choice Model for Assortment Optimization](https://mlsanity.com/paper/2308.05617/) (2023)
- [Designing Graph Convolutional Neural Networks for Discrete Choice with Network Effects](https://mlsanity.com/paper/2503.09786/) (2025)
- [Attitudes and Latent Class Choice Models using Machine learning](https://mlsanity.com/paper/2302.09871/) (2023)
- [Computer vision-enriched discrete choice models, with an application to residential location choice](https://mlsanity.com/paper/2308.08276/) (2023)
- [Images in Discrete Choice Modeling: Addressing Data Isomorphism in Multi-Modality Inputs](https://mlsanity.com/paper/2312.14724/) (2023)
- [Bayesian Deep Learning for Discrete Choice](https://mlsanity.com/paper/2505.18077/) (2025)
- [Better Capturing Interactions Between Products in~Retail: Revisited Negative Sampling for~Basket Choice Modeling](https://mlsanity.com/paper/2610.17963/) (2026)

## Abstract (arXiv)

This study proposes a novel approach that combines theory and data-driven choice models using Artificial Neural Networks (ANNs). In particular, we use continuous vector representations, called embeddings, for encoding categorical or discrete explanatory variables with a special focus on interpretability and model transparency. Although embedding representations within the logit framework have been conceptualized by Pereira (2019), their dimensions do not have an absolute definitive meaning, hence offering limited behavioral insights in this earlier work. The novelty of our work lies in enforcing interpretability to the embedding vectors by formally associating each of their dimensions to a choice alternative. Thus, our approach brings benefits much beyond a simple parsimonious representation improvement over dummy encoding, as it provides behaviorally meaningful outputs that can be used in travel demand analysis and policy decisions. Additionally, in contrast to previously suggested ANN-based Discrete Choice Models (DCMs) that either sacrifice interpretability for performance or are only partially interpretable, our models preserve interpretability of the utility coefficients for all the input variables despite being based on ANN principles. The proposed models were tested on two real world datasets and evaluated against benchmark and baseline models that use dummy-encoding. The results of the experiments indicate that our models deliver state-of-the-art predictive performance, outperforming existing ANN-based models while drastically reducing the number of required network parameters.