Learning Causal Network Structure With Interventional Data

Bayesian network, also called belief network, is a probabilisticgraphic model, it represents a set of variables and their conditionaldependence via a directed acyclic graph. A causal network is a Bayesiannetwork with an explicit requirement that the relationships be causal,which can be used to model real black box system.In reality, we often have to explore the structure of some unknownsystem from scratch, this is a typical causal network structure learningproblem. For example, a disease diagnosis system can be taken as anetwork which consists of nodes that represent whether a patient has somesymptoms and nodes that represent whether a patient has some pathogeny,several pathogenies can have the same symptom by chance, and onepathogeny can have several symptoms by chance, so this system can beviewed as a probabilistic causal network. The problem of discovering thestructure of some unknown system is very common in many fields, and ifany method can find the true structure of that, then many useful inferencesand predictions can be made.We first define two types of data:1) observational data. Observationaldata is samples of a system in natural environment. Each sample consistsof random values on each attribute.2) interventional data. Interventionaldata is samples of a system under intervention. The states of someparticular nodes are under complete control of itself, rather than its parentnodes. Observational data is easy to get, but with some interventional data,some ambiguous causal directions between two nodes can be moreprecisely resolved.Methods in the literature can be divided into two categories:1)methods based on dependency analysis.2) Methods based on―score and search". They were mostly based on observational data, besides possiblysome prior knowledge. There exists a theoretical limit on structure learningfrom observational data: even with infinitely many samples, we cannotresolve the structures in an equivalence class. Without perturbationexperiments this situation can not be further resolved.To address this problem, a new algorithm for causal network structurelearning with interventional data is proposed. With the incorporation ofinterventional data, we adapt the traditional BDeu scoring method, and doMCMC searches to get the causal network with the highest score as ouranswer. Experiments show that, this new algorithm can get a sufficientlyprecise causal network in affordable time.