Parameter and Structure Learning in Nested Markov Models
By Ilya Shpitser, Thomas S. Richardson, James M. Robins, Robin J. Evans. 2012
26 citations recorded by the source corpus.
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a 'fixing' operation, in which a joint distribution is divided by a conditional. This operation generalizes marginalizing and conditioning. Some of these constraints correspond to identifiable 'dormant' independence constraints, with the well known 'Verma constraint' as one example. Recently, models defined by a set of the constraints arising after fixing from a DAG with latents, were characterized via a recursive factorization and a nested Markov property. In addition, a parameterization was given in the discrete case. In this paper we use this parameterization to describe a parameter fitting algorithm, and a search and score structure learning algorithm for these nested Markov models. We apply our algorithms to a variety of datasets.
Subfields: Artificial Intelligence
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Mathias Drton
- Marloes H. Maathuis
- Robin J. Evans
- Thomas S. Richardson
- Nicolai Meinshausen
- Diego Colombo
- Peter Buhlmann
- Preetam Nandy
Citations in the corpus
- Structure Learning in Graphical Modeling (2016, methodology): “To represent constraints beyond conditional independencies, there is current work on new classes of graphs, including nested Markov models (Shpitser et al., 2012, 2014) and mDAGs (Evans, 2016).”
- Margins of discrete Bayesian networks (2015, methodology): “s considering marginal and nested models for DAGs have used acyclic directed mixed graphs, which are the restriction of mDAGs with random verticessothat eachbidirected edgehassizetwo(Richardson,2003; Shpitser et al., 2012; Evans and Richardson, 2014; Richardson et al., 2017). From the perspective of”
- Graphical methods for inequality constraints in marginalized DAGs (2012, background): “Recent work by [9] characterizes equality constraints in marginalized DAG models in terms of graphical operations, which are easily adapted to a separation criterion.”