The Strong And Weak Identifiability In Causal Discovery

Exploring and discovering the causal relations among things are core issues in scientific research.The standard gold of such exploration and discovery is to conduct randomized controlled trials(RCTs).However,RCTs often have limitations in practical including expensive cost,limited participation group,and ethical issues.Therefore,discovering causal relations from passively observed data is an essential problem.Indeed,causal discovery methods based on passive observed data have made great progress in the past decades and have been widely used in various fields and such methods have become an unignorable way to discover causal relations.In this kind of method,a core concept is identifiability i.e.,whether the discovered causal model is unique.If so,this causal model is called identifiable,otherwise it’s non-identifiable.A natural and essential question is: For all identifiable causal models,whether they are of the same difficulty to identify? This paper focuses on this question and the main contents and contributions of this paper include:1.For non-linear additive noise model which is identifiable,we point out that the difficulty of identification is different,we then propose to further divide the identifiable causal models into strongly identifiable and weakly identifiable ones according to the difficulty of identification,we also give theoretical definition and criteria with proof.Besides,this paper reveals the relationship between the strength of identifiability and two metrics commonly used in causal discovery: the goodness of fit and the independence of residual.We further points out that due to the ignorance of this point,existing causal discovery methods can only deal with one of the two types(strongly or weakly identifiable)of the problem.2.To cope with the issue that existing causal discovery methods can only handle one of the two types(strongly or weakly identifiable)of the problem,this paper propose a unified framework named GENIUS(A Generic Framework for Non-linear Causal Discovery)for both strongly and weakly identifiable problems.Experiments on synthetic data demonstrate the effectiveness of GENIUS far beyond existing methods.3.In this paper,GENIUS is applied to two real-world problem scenarios,namely,the discovery of the causal relations between the expression levels of various sub-stances in the protein signaling network in bioinformatics which is a traditional causal discovery problem and the discovery of the causal relations between the knowledge concepts mastered by students in the field of intelligent education which aims to help students find the weakness in their knowledge system.Experiments on these real-world problems demonstrate that GENIUS is far more effective on causal discovery than other methods.