# Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions

arXiv: https://arxiv.org/abs/2301.00801 · HTML: https://mlsanity.com/paper/2301.00801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 2 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Regularly random duality](https://mlsanity.com/paper/1303.7295/) (2013)
- [Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption](https://mlsanity.com/paper/1808.05293/) (2018)
- [Upper-bounding ℓ1-optimization weak thresholds](https://mlsanity.com/paper/1303.7289/) (2013)
- [Randomization Tests in Observational Studies with Staggered Adoption of Treatment](https://mlsanity.com/paper/1912.10610/) (2019)

## Abstract (arXiv)

In this paper, we revisit and further explore a mathematically rigorous connection between Causal inference (C-inf) and the Low-rank recovery (LRR) established in [10]. Leveraging the Random duality - Free probability theory (RDT-FPT) connection, we obtain the exact explicit typical C-inf asymmetric phase transitions (PT). We uncover a doubling low-rankness phenomenon, which means that exactly two times larger low rankness is allowed in asymmetric scenarios compared to the symmetric worst case ones considered in [10]. Consequently, the final PT mathematical expressions are as elegant as those obtained in [10], and highlight direct relations between the targeted C-inf matrix low rankness and the time of treatment. Our results have strong implications for applications, where C-inf matrices are not necessarily symmetric.