# Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data

arXiv: https://arxiv.org/abs/2307.10515 · HTML: https://mlsanity.com/paper/2307.10515/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2023.

## Built on by (most cited first, 17 of 17)

- [Quantifying Knowledge Distillation Using Partial Information Decomposition](https://mlsanity.com/paper/2411.07483/) (2024)
- [Towards Formalizing Spuriousness of Biased Datasets Using Partial Information Decomposition](https://mlsanity.com/paper/2407.00482/) (2024)
- [Partial Information Decomposition via Normalizing Flows in Latent Gaussian Distributions](https://mlsanity.com/paper/2510.04417/) (2025)
- [Massively Multimodal Foundation Models: A Framework for Capturing Interactions with Specialized Mixture-of-Experts](https://mlsanity.com/paper/2509.25678/) (2025)
- [SOmegaI: Score-based O-INFORMATION Estimation](https://mlsanity.com/paper/2402.05667/) (2024)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [Auditing Language Model Unlearning via Information Decomposition](https://mlsanity.com/paper/2601.15111/) (2026)
- [Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition](https://mlsanity.com/paper/2502.10878/) (2025)
- [Explainable Multimodal Regression via Information Decomposition](https://mlsanity.com/paper/2512.22102/) (2025)
- [Learning Invariant Graph Representations Through Redundant Information](https://mlsanity.com/paper/2512.06154/) (2025)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)
- [Synergistic Information Disentanglement for Omni-modal Slide Representation Learning in Computational Pathology](https://mlsanity.com/paper/2609.02118/) (2026)
- [ALICE: In-context, Zero-shot, Mutual Information Estimation](https://mlsanity.com/paper/2609.34962/) (2026)
- [Structured Latent Modeling for Supervised Multimodal Information Decomposition](https://mlsanity.com/paper/2609.35502/) (2026)
- [Interpreting Reasoning of Large Language Models via Partial Information Decomposition](https://mlsanity.com/paper/2610.00571/) (2026)
- [Gaussian BROJA Partial Information Decomposition in Closed Form](https://mlsanity.com/paper/2610.13464/) (2026)
- [Are Multimodal Benchmarks Really Useful? Item-Level Multimodal Benchmark Diagnosis via Structure-Response Co-Calibration](https://mlsanity.com/paper/2610.14542/) (2026)

## Abstract (arXiv)

Recent advances in neuroscientific experimental techniques have enabled us to simultaneously record the activity of thousands of neurons across multiple brain regions. This has led to a growing need for computational tools capable of analyzing how task-relevant information is represented and communicated between several brain regions. Partial information decompositions (PIDs) have emerged as one such tool, quantifying how much unique, redundant and synergistic information two or more brain regions carry about a task-relevant message. However, computing PIDs is computationally challenging in practice, and statistical issues such as the bias and variance of estimates remain largely unexplored. In this paper, we propose a new method for efficiently computing and estimating a PID definition on multivariate Gaussian distributions. We show empirically that our method satisfies an intuitive additivity property, and recovers the ground truth in a battery of canonical examples, even at high dimensionality. We also propose and evaluate, for the first time, a method to correct the bias in PID estimates at finite sample sizes. Finally, we demonstrate that our Gaussian PID effectively characterizes inter-areal interactions in the mouse brain, revealing higher redundancy between visual areas when a stimulus is behaviorally relevant.