Template model for Bayesian network

Template variable X(U1,U2,...,Uk) is instantiated (duplicated) multiple times.Template models: languages that specify how variables inherit dependency model from templateDynamic Bayesian networksObject-relational models: Directed: plate modelsUndirectedMarkov assumption (X(t+1)⊥X(0:t−1)|X(t)) P(X(0:T))=P(X(0))∏t=0T−1P(X(t+1)|X(0:t))=P(X(0))∏t=0T−1P(X(t+1)|X(t)) Time Invariance For all t , P(X(t 1)|X(t))=P(X′|X)2-time-slice Bayesian network A tranisition model (2TBN) over X1,X2,…,Xn is specified as a BN fragment such that: The nodes include X′1,X′2,…,X′n and a subset of X1,X2,…,Xn Only the nodes X′1,X′2,…,X′n have parents and a CPDThe 2TBN defines a conditional distribution P(X′|X)=∏i=1nP(X′i|PaX′i) Dynamic Bayesian network A dynamic Bayesian network over X1,…,Xn is defined by a 2TBN BN→ over X1,…,Xn a Bayesian network BN(0) over X(0)1,…,X(0)n Ground Network For a trajectory over 0,…,T we define a ground (unrolled network) such that The dependency model for X(0)1,…,X(0)n is copied from BN(0) The dependency model for X(t)1,…,X(t)n for all t>0 is copied from BN→