Hypergraph-based Causal Modeling
Abstract
Probabilistic graphical models (PGMs), such as Bayesian networks and chain graphs, are compact representations of independence relat"ions that hold in a domain. PGMs have been very successfully used for representing causal relations and to support the discovery of" causal dependence: for example, whether smoking causes cancer, or whether drug A is effective on disease B, etc. However, PGMs are"" restricted in their ability to represent useful domain information by various restriction on their structure. For example, a Bayesi""an network structure cannot represent a situation in which two variables, say A and B, are conditionally independent given two other"" variables, say C and D, which are in turn unconditionally independent. These limitations have led to a plethora of PGMs with additi"onal kinds of edges.Intellectual merit: We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call ~Bayesian hypergraphs~ (a generalization of Bayesian networks and chain graphs). The new framework has the following advan"tages. First, correlational and causal dependencies are distinguished but co-exist via directed hyperedges: causal dependencies are"" between heads and tails while correlational dependences are among head vertices. Second, Bayesian hypergraphs can encode graphicall"y many more independence and functional structuresthan graph-based PGMs. This generality will help support structure learning bette"r, without the need to resort to additional intermediate representations. Third, methodologies from the area of prediction and causa""l reasoning can be tested and applied to the area of learning naturally by sharing the same mathematical object. In particular, we c""an combine learning and intervention. Finally, by leveraging new developments on hypergraph theory, one may reduce the computational" cost of structure learning via reduction and approximation at the global level.Broader impact: As this project investigates and d"evelops a principled theory that combines the power of causal models and deep learning models, it has potential to benefit many fiel""ds, such as information extraction and analysis, speech recognition, computer vision, drug discovery and toxicology, customer relati""onship management, and bioinformatics. The investigators will continue the training of Ph.D. students at a high level, introducing t"hem to interdisciplinary and international research collaboration.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 01, 2017
- Source ID
- N000141712842
Entities
People
- Linyuan Lu
Organizations
- Office of Naval Research
- United States Navy
- University of South Carolina