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Incorporating Causal and Associative Prior Knowledge when Learning Causal Models
Χρήση αιτιατής και εξαρτησιακής πρότερης γνώσης για την κατασκευή αιτιατών μοντέλων
Μπορμπουδάκης, Γεώργιος Νικόλαος
Τσαμαρδινός, Ιωάννης
Causal graphical models, such as Causal Bayesian Networks, are widely used to model the dependency
structure, as well as causal relations among variables of interest. There are multiple
approaches to learn such models from data; however, most methods do not take available prior
knowledge into consideration when learning a model, or consider certain types of prior knowledge
that are not often available in practice. Prior knowledge often comes in the form of knowledge
about causal or associative relations between pairs of variables. Such relations correspond to
certain paths in a causal model. This type of knowledge naturally stems from domain experts,
as well as observational and experimental data, among others. We develop theory and methods
that use causal and associative prior knowledge when learning causal models. We approach the
problem from two different perspectives.
First, we consider the case of prior knowledge in the form of facts about the presence or
absence of causal paths, and develop algorithms that incorporate it into existing causal models.
Specifically, we consider the formalisms of Causal Bayesian Networks and Maximal Ancestral
Graphs and their Markov equivalence classes: Partially Directed Acyclic Graphs and Partially
Oriented Ancestral Graphs. We characterize the equivalence class of all graphs that belong in
a Markov equivalence class and are consistent with a set of causal prior knowledge. We then
introduce sound and complete procedures to incorporate causal knowledge in such models. In
simulated experiments we show that our methods can make a large number of new inferences,
even with a few prior knowledge facts.
Subsequently, we consider knowledge in the form of prior beliefs (that is, having a degree
of uncertainty) on certain causal or associative relations. We present a method that uses such
beliefs to assign priors to all possible network structures, which can then be used by any searchand-
score based method for learning graphical models. We also propose a novel search-operator
to take further advantage of the prior beliefs. In contrast to previous approaches, our method can
handle the case of dependent and possibly incoherent prior beliefs. In simulated proof-of-concept
experiments we show that our method can indeed take advantage of prior knowledge, and that
the proposed search-operator can significantly improve the quality of the learned models
(EN)
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