An Interactive Approach for Bayesian Network Learning Using Domain or Expert Knowledge - 2013

Title : An Interactive Approach for Bayesian Network Learning Using Domain or Expert Knowledge Author(s): Masegosa, Andrés R. and Moral, Serafín Link(s) : https://linkinghub.elsevier.com/retrieve/pii/S0888613X13000698

Existing techniques for introducing expert knowledge ask for priors - expert does not do anything after they provide their knowledge.

This paper wants to overcome this, and make this process interactive - this should be done in a way that experts are asked about conflictive edges.

Method currently presented only for multinomial Bayesian Networks (BNs).

Graph represented as a vector \(G=(\Pi_1,\cdots,\Pi_n)\) where \(\Pi_i\) is the parent set of variable \(X_i\). Assuming a Dirichlet prior gives the marginal likelihood \(P(\text{Data}|G)\) in closed form. A specific prior is chosen for the graph structure to account for what is called multiplicity correction.

The interactive method proposed decomposes the learning process into:

• A learning process focused on learning the skeletion - built by combining Markov boundaries of each variable, independently induced from data using expert knowledge.
• Use expert knowledge to learn DAGs contrained by the skeleton from before - assumes the expert can answer whether two edges are connected or not.
• Use expert knowledge to learn DAGs not constrained by the skeleton from before.

\(T\) is the total number of possible edges, \(m_k\in \{-1,0,1\}\) depending on state (presence and/or direction) of edge \(k\), \(m_k^e\) is information provided by expert about \(m_k\). Expert reliability for edge \(k\) is denoted \(R_k\). \(A(k)\) is the binary decision variable representing whether to ask the expert about edge \(k\) or not, and this decision has an associated utility \(U(k)\).

Experiments are as follows: Synthetic data from 5 common BNs like the Alarm network. Expert is assumed to be an oracle, i.e. always returns correct edge information.

Evaluation involves comparing:

• No expert.
• Interaction done only about the DAG structure and not the skeleton.
• Interaction is done first on skeleton, then DAG structure, with interaction stopping if information gain is below a specific threshold.
• Same as above but a different threshold level.