Cause-effect pair methods might extend the potential outcome framework to resolve cases with no a priori on causal direction X → Y or X ← Y . All is needed is to first condition P ( X , Y ) on known potential confounders Z (e.g. age, gender, etc.) or adjust with a propensity score to get P ( X , Y | Z ), then address edge orientation as a cause-effect pair problem. 

The setting of cause-effect pairs, making no a priori assumption on causal orientation nor on the presence of hidden confounders, lends itself to applications in areas like epidemiology, when it is unclear which variable is the “treatment” and which one is the “outcome”, e.g. X = diabetes_consumption and Y = drinking_diet _soda .

Practical (the primary justification)

One may argue that the cause-effect pair problem is of fundamental scientific interest. Indeed, it is the smallest problem addressing the issue of finding asymmetries in joint distributions of variables that are potentially revealing of causal relationships, and it cannot be resolved using Markov properties (conditional independence testing). 

Fundamental Scientific Interest

Basing causal discovery on cause-effect pairs may help fighting against the “curse of dimensionality” by avoiding to perform extensive conditional independence tests, which are very data hungry. 

Low Dimensionality of Cause-Effect Pair Method

Why considering only pairs of variables?

There are multiple justifications to embrace the cause-effect pair setting. 
 - Practical (the primary justification)
 - Fundamental Scientific Interest
 - Low Dimensionality

However, what is gained on one side might be lost on another and ultimately, so it is better to think of pairwise methods as complements to multi-variate graphical model methods that help orienting edges left un-oriented in Markov equivalence classes.

University of Michigan - Ann Arbor

Telling cause from effect from purely observational data (focusing on pairs (X,Y) of variables rather than multi-variate case) has been a challenge at the NIPS 2008 workshop on Causality.  The scenario can be described as follows: 
 - Given observations $( x_1 , y_1 ), …, ( x_k , y_k )$ iid (independent and identically distributed) drawn from some distribution $P_{X , Y}$ , infer whether X causes Y (a) or Y causes X (b) , given the promise that exactly one of these alternatives is true. 

The NIPS 2013 challenge extended this setting to three classes:
$X\rightarrow Y (a)$ , $Y\rightarrow X (b)$, or the null class $\{(c),(d)\}$, which consisted of the unconnected case $X Y$ or the case of pure confounding $X \leftrightarrow Y$ (this notation is used as shorthand for X ← H → Y , where H is unobserved, but where neither X or Y cause each other). 

Cause-Effect Pair Challenge

 Isabelle Guyon, Alexander Statnikov, Berna Bakir Batu (2019)
Cause Effect Pairs in Machine Learning (The Springer Series on Challenges in Machine Learning)
https://www.amazon.com/Effect-Machine-Learning-Springer-Challenges/dp/3030218090

Cause Effect Pairs in Machine Learning

Justifications to Embrace the Cause-Effect Pair Setting

Cause-effect methods can be divided into two types:
 - Generative Models 
 - Discriminative Models

Cause-Effect Methods

There are two important extensions of the cause-effect pair problem:
 - Causal discovery methods for time series
 - Going beyond the treatment of two variables (triplet and more)

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