# Error Probability Bounds for Invariant Causal Prediction via Multiple Access Channels

arXiv: https://arxiv.org/abs/2308.10119 · HTML: https://mlsanity.com/paper/2308.10119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2023.

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

- [Mining Invariance from Nonlinear Multi-Environment Data: Binary Classification](https://mlsanity.com/paper/2404.15245/) (2024)

## Abstract (arXiv)

We consider the problem of lower bounding the error probability under the invariant causal prediction (ICP) framework. To this end, we examine and draw connections between ICP and the zero-rate Gaussian multiple access channel by first proposing a variant of the original invariant prediction assumption, and then considering a special case of the Gaussian multiple access channel where a codebook is shared between an unknown number of senders. This connection allows us to develop three types of lower bounds on the error probability, each with different assumptions and constraints, leveraging techniques for multiple access channels. The proposed bounds are evaluated with respect to existing causal discovery methods as well as a proposed heuristic method based on minimum distance decoding.