The authors can cast the cause-effect pair problem as a regular machine learning classification problem in which input-output pairs $( P_{Π = π} ( X , Y )$, G = g ) are drawn randomly and independently from a $\textbf{“mother distribution” }$ $P_M( P_{Π = π} ( X , Y ), G = g )$, then divided into training and test sets. 

The problem is to “classify” distributions $P_{Π = π} ( X , Y )$ into one of four classes $g ∈ \{ X → Y , X ← Y , X \leftrightarrow Y , X ⊥ Y \} $

Cast Cause-Effect Pair Problem as Machine Learning Classification Problem

Discriiminative algorithms do not attempt to reverse engineer the data generating process, they merely classify the empirical joint distribution of two variables $X$ and $Y$ (a scatter plot) as being a $X$ cause $Y$ or a $Y$ cause $X$ (or neither).

University of Michigan - Ann Arbor

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

Cause-Effect Methods

 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

Discriminative Models for Cause-Effect Problem

Generative algorithms solve the cause-effect pair problem from a reverse engineering perspective: given the available measurements $\{ (x_i,y_i) \}_{i=1}^n $ of the two variables $X$ and $Y$, the task is to discover the underlying causal process that led the variables to take the values they have.

Such methods allow gaining not only a clue about the causal direction but also information about the mechanism itself, making causal discovery less of a black box decision process.

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