{"articles":{"markov-network-why@graphical-networks":{"content":"<p>Given a (possible large) set of variables, one may ask: which variables influence other variables, and which ignore each other? And: could we use this information to simplify the computations involving the distribution? <br> For a distribution \\({P({\\mathcal{X}}{})}\\), <br> From the opposite perspective, we look for dependences instead of independences. <br> It turns out that given a set of independences, <br> If we choose to represent no indepdences, <br> Notice that when we do not consider any structural information at all, we do not have any independences; and we have all possible dependences between every node. As we add or obtain structural information, we add independences or equivalently remove possible dependences. So it is the independences that are considered \"valuable\"; they are what allows us to simplify the distribution, while dependences complicate it. <br> A Markov network lets us represent these independences using an undirected graph: nodes that are part of the same clique are considered to be dependent. So there is an equivalence between the independences/dependences,</p>","names":[[["Why Markov networks",""]]]}},"style":"Note"}