Conditions are presented for local identifiability of discrete undirected graphical models with a binary hidden node. These models can be obtained by extending the latent class model to allow for conditional associations between the observed variables. The conditions are based on the topology of the undirected graph and rely on the faithfulness assumption. For models that are not locally identified we derive the expression of the parameter (sub)space where the identifiability breaks down. This in turn allows us (a) to find a reparametrization that leads to an identified model and (b) to compute the dimension of the model. Extensions to more than one hidden node can be derived by exploiting the factorization of the joint distribution dictated by the graph.
On the identification of discrete graphical models with hidden nodes
STANGHELLINI, Elena;
2010
Abstract
Conditions are presented for local identifiability of discrete undirected graphical models with a binary hidden node. These models can be obtained by extending the latent class model to allow for conditional associations between the observed variables. The conditions are based on the topology of the undirected graph and rely on the faithfulness assumption. For models that are not locally identified we derive the expression of the parameter (sub)space where the identifiability breaks down. This in turn allows us (a) to find a reparametrization that leads to an identified model and (b) to compute the dimension of the model. Extensions to more than one hidden node can be derived by exploiting the factorization of the joint distribution dictated by the graph.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
