# BROJA-2PID: A robust estimator for bivariate partial information decomposition

arXiv: https://arxiv.org/abs/1802.02485 · HTML: https://mlsanity.com/paper/1802.02485/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2018.

## Built on by (most cited first, 6 of 6)

- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [A Rigorous Information-Theoretic Definition of Redundancy and Relevancy in Feature Selection Based on (Partial) Information Decomposition](https://mlsanity.com/paper/2105.04187/) (2021)
- [Partial Information Decomposition for Data Interpretability and Feature Selection](https://mlsanity.com/paper/2405.19212/) (2024)
- [A Generalized Information Bottleneck Theory of Deep Learning](https://mlsanity.com/paper/2509.26327/) (2025)
- [Dissipation alters modes of information encoding in small quantum reservoirs near criticality](https://mlsanity.com/paper/2412.18290/) (2024)
- [Interaction-Aware Sensitivity Analysis for Aerodynamic Optimization Results using Information Theory](https://mlsanity.com/paper/2112.05609/) (2021)

## Abstract (arXiv)

Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decompostion (BROJA PID) measure [1]. We developed a production-quality robust software that computes the BROJA PID measure based on the Cone Programming model. In this paper, we prove the important property of strong duality for the Cone Program and prove an equivalence between the Cone Program and the original Convex problem. Then describe in detail our software and how to use it.newlineindent