Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection beten information geometry and order theory leads to efficient decomposition algorithms. This generalization of Amari's seminal work on hierarchical decomposition of probability distributions on event combinations enables us to analyze high-order statistical interactions arising in neuroscience, biology, and machine learning.
['Mahito Sugiyama', 'Hiroyuki Nakahara', 'Koji Tsuda']
I am writing a research paper on a idea Information decomposition on structured space
[{"from": "human", "value": "I am writing a research paper on a idea Information decomposition on structured space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection beten information geometry and order theory leads to efficient decomposition algorithms. This generalization of Amari's seminal work on hierarchical decomposition of probability distributions on event combinations enables us to analyze high-order statistical interactions arising in neuroscience, biology, and machine learning."}]