5.2 Restricted Boltzmann Machine
5.2.1 The RBM as an energy-based model
The RBM corresponds to a special structure of such a graph, called bipartite, where the set V of vertices can be split into two groups of visible vertices VV and hidden vertices VH such that the set E of edges only consists of elements of the form {v,h}∈VV ×VH. Figure 5.1 provides a schematic representation of the RBM that implements the bipartite graph structure. This in particular implies that cliques can only be of size one (all the singleton nodes) or two (all the pairs (v,h) in VV ×VH). For simplicity, we shall denote v an element of X|VV | and h an element of X|VH|, and identify the random variable X with the vertices. The following lemma gives us the general form of the energy function (5.1) for RBMs:
Lemma 6 (RBM Energy Lemma). In a Restricted Boltzmann Machine, the energy function takes the form
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for any v := (v1,…,vN...
