# Neural Networks for Latent Budget Analysis of Compositional Data

arXiv: https://arxiv.org/abs/2109.04875 · HTML: https://mlsanity.com/paper/2109.04875/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Activation Functions: Comparison of trends in Practice and Research for Deep Learning](https://mlsanity.com/paper/1811.03378/) (2018)
- [Correspondence Analysis Using Neural Networks](https://mlsanity.com/paper/1902.07828/) (2019)

## Built on by (most cited first, 1 of 1)

- [Simultaneous Latent Budget Trees for Stratified Classification](https://mlsanity.com/paper/2606.13295/) (2026)

## Abstract (arXiv)

Compositional data are non-negative data collected in a rectangular matrix with a constant row sum. Due to the non-negativity the focus is on conditional proportions that add up to 1 for each row. A row of conditional proportions is called an observed budget. Latent budget analysis (LBA) assumes a mixture of latent budgets that explains the observed budgets. LBA is usually fitted to a contingency table, where the rows are levels of one or more explanatory variables and the columns the levels of a response variable. In prospective studies, there is only knowledge about the explanatory variables of individuals and interest goes out to predicting the response variable. Thus, a form of LBA is needed that has the functionality of prediction. Previous studies proposed a constrained neural network (NN) extension of LBA that was hampered by an unsatisfying prediction ability. Here we propose LBA-NN, a feed forward NN model that yields a similar interpretation to LBA but equips LBA with a better ability of prediction. A stable and plausible interpretation of LBA-NN is obtained through the use of importance plots and table, that show the relative importance of all explanatory variables on the response variable. An LBA-NN-K- means approach that applies K-means clustering on the importance table is used to produce K clusters that are comparable to K latent budgets in LBA. Here we provide different experiments where LBA-NN is implemented and compared with LBA. In our analysis, LBA-NN outperforms LBA in prediction in terms of accuracy, specificity, recall and mean square error. We provide open-source software at GitHub.