Unknown Structure

When we do not know the structure of the network, we have to do model selection . We learn the structure by generating a model space, and by evaluating the models by using a metric with respect to a database D. We select the model that fits the data best.

One existing metric is the Bayesian Information Criterion: [19]

$$BIC(S_m\vert sample) = -\log P(sample\vert\hat{\theta_m},S_m) + \frac{1}{2}dim(\theta_m) \log N$$

$\hat{\theta_m}$ is the maximum likelihood estimate of $\theta_m$ in structure S_m. N is the sample size and dim($\theta_m$) the dimensionality.

Several other metrics exist for evaluating the network:

• AIC - A Information Criterion
• MAP - Maximum a Posteriori