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Causal structure learning and inductive inference based on Kolmogorov complexity This publication appears in: Dagstuhl Seminar Proceedings Authors: J. Lemeire Publication Date: Oct. 2009
Abstract: These are the results of an analysis of current causal structure learning with the general principles for inductive inference based on Kolmogorov complexity. The principle is that patterns in data do not appear by accident, but reveal some of the structure of the system under study. In causal terms: patterns point to mechanisms. First I will to put forward a new condition, namely the Independence of Conditionals (IC). Causal structure learning through Bayesian networks comes to the mapping of the Conditional Probability Distributions (CPDs) of a factorization to the mechanisms of the underlying system. Causal mechanisms are modular components which can be changed independently. I will argue that, besides local minimality, the fundamental condition for drawing such causal conclusions is the algorithmic independence of the CPDs, which we called the IC condition. Violation of IC gives indications about non-global minimality of the model or the presence of metamechanisms. When IC holds for a factorization, the factorization gives you the top-ranked causal hypothesis. It is the hypothesis that should be considered first. But no guarantee of its correctness can be given, since the factorization only describes the behavior of the system under study and the system could be more complex then its behavior suggests. I will argue that IC is more fundamental than faithfulness. First, because the IC condition provides inference rules beyond independence-based learning algorithms. The condition applies for any decomposition, like for example additive noise models in which the CPDs are further decomposed. Secondly, some violations of faithfulness, such as deterministic relations, do not violate IC and should not hinder causal structure learning. Nonetheless, I believe that faithfulness describes an important property of a model. Generally speaking, faithfulness says that the qualitative properties of a system are described by the qualitative part of the model. And this was Pearl's clear intention when creating the Bayesian network approach. External Link.
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