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

TL;DR

This paper establishes a rigorous mathematical connection between causal inference and low-rank recovery, revealing new phase transition phenomena and implications for asymmetric scenarios in causal inference matrices.

Contribution

It introduces explicit asymmetric phase transition formulas for causal inference, extending previous symmetric case results and uncovering a doubling low-rankness phenomenon.

Findings

Derived exact asymmetric phase transition expressions

Discovered doubling low-rankness phenomenon in asymmetric scenarios

Linked low rankness to treatment duration in causal inference

Abstract

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.