Application of the Information Bottleneck to LPAD Learning

In order to apply the Information Bottleneck (IB) to LPADs, the network Gout is the result of the translation of the LPAD for which we want to learn the parameters plus the addition of the Y variable. The set of hidden variables contains the vector of the choice variables CH plus those atoms that are unobserved in the data, let us call them T. With X we indicate the set of atom variables that are observed in the data. Suppose you want to learn the parameters of an LPAD using IB. Consider the LPAD L: r1 = x1 : 0.4 ∨ x2 : 0.3. r2 = x2 : 0.1 ∨ x3 : 0.2. r3 = x4 : 0.6 ∨ x5 : 0.4 ← x1. r4 = x5 : 0.4 ← x2, x3. r5 = x6 : 0.3 ∨ x7 : 0.2 ← x2, x5. The Bayesian network equivalent to L is shown in Figure 1. In order to apply IB to LPADs, the