Assumptions for Causal Discovery

Abstract

I will list up some assumptions when a casual model is considered here. Also, several causal learning method corresoponding to mentioned assumptions will be introduced.

Markov assumption

$X_{i}$ is an observational varibale. $X_{i} \perp X_{j} \mid Pa(X_{i})$, where $X_{i}$ is a non-descendant of $X_{i}$ and $Pa(X_{i})$ represent the set of parents of $X_{i}$.

Faithfulness assumption

Let $I(G)$ and $I(P)$ be the set of independence relations in a casual graph, and the set of independence relations in the correponding distribution. If $I(G) = I(P)$, then we say that the graph $G$ is faithful to the distribution $P$.

LiNGAM asssumption

• The causal effects are linear.
• The distributions of disturbance terms (noise terms) are non-Gaussian.
• The distributions are continuous.
• Exogenous variables are mutually independent.

Sufficiency

All varibales in a causal system have been observed.

Measurement assumption

There is no observed variable who is an ancestor of a latent variable.

canonical LvLiNGAM

• LiNGAM
• All latent variables are mutually independent.

purity assumption

There is no directed path (ancestral relationship) between a pair of observed variables.