Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of decomposing a multivariate probability distribution p(v) defined over a set of random variables V =fV1;:::;Vng into a product of factors defined over disjoint subsets fVF1;:::;VFmg.  show that the decomposition of V into irreducible disjoint factors forms a unique partition, which corresponds to the connected components of a Bayesian or Markov network, given that it is faithful to p. Finally,  provide three generic procedures to identify these factors withO(n 2 ) pairwise conditional independence tests (Vi??VjjZ) under much less restrictive
['Maxime Gasse', 'Alex Aussem']
I am writing a research paper on a idea Identifying the irreducible disjoint factors of a multivariate probability distribution
[{"from": "human", "value": "I am writing a research paper on a idea Identifying the irreducible disjoint factors of a multivariate probability distribution"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the problem of decomposing a multivariate probability distribution p(v) defined over a set of random variables V =fV1;:::;Vng into a product of factors defined over disjoint subsets fVF1;:::;VFmg.  show that the decomposition of V into irreducible disjoint factors forms a unique partition, which corresponds to the connected components of a Bayesian or Markov network, given that it is faithful to p. Finally,  provide three generic procedures to identify these factors withO(n 2 ) pairwise conditional independence tests (Vi??VjjZ) under much less restrictive"}]