# Learning Sparse Latent Representations with the Deep Copula Information Bottleneck

arXiv: https://arxiv.org/abs/1804.06216 · HTML: https://mlsanity.com/paper/1804.06216/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2018.

## Built on by (most cited first, 9 of 9)

- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Stochastic Encodings for Active Feature Acquisition](https://mlsanity.com/paper/2508.01957/) (2025)
- [CRAFT: Adapting VLA Models to Contact-rich Manipulation via Force-aware Curriculum Fine-tuning](https://mlsanity.com/paper/2602.12532/) (2026)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Learning Channel Importance for High Content Imaging with Interpretable Deep Input Channel Mixing](https://mlsanity.com/paper/2308.16637/) (2023)
- [Learning Conditional Invariance through Cycle Consistency](https://mlsanity.com/paper/2111.13185/) (2021)
- [Learning Generative Prior with Latent Space Sparsity Constraints](https://mlsanity.com/paper/2105.11956/) (2021)
- [A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction](https://mlsanity.com/paper/2601.19175/) (2026)
- [Towards Dual-Brain Minimal Sufficient Representation for Vision-Language Navigation](https://mlsanity.com/paper/2607.23181/) (2026)

## Abstract (arXiv)

Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.