In this approach, the basic postulate that “the factorization of the joint density function $P_{cause,effect}$ into $P_{cause} P_{effect|cause}$ should lead to a simpler model than $P_{effect} P_{cause|effect}$ ”, can be expressed with the Kolmogorov complexity framework: $K(P_{cause}) + K(P_{effect|cause}) \overset{+}\leq K(P_{effect}) + K(P_{cause|effect})$

This inequality comes from the postulate of algorithmic independence between the distribution of the cause $P_{cause}$ and the distribution of the causal mechanism $P_{effect|cause}$ stated by Janzing and Schölkopf as: $I(P_{cause} : P_{effect|cause}) \overset{+}=0$ where $I(P_{cause} : P_{effect|cause})$ denotes algorithmic mutual information.

Kolmogorov complexity and algorithmic mutual information are not computable in practice but they have led to two different practical implementations in the literature:

• Model Selection with Minimum Message Length Principle (MML)
• Independence Between Cause and Mechanism