Independencies Induced from a Graphical Markov Model After Marginalization and Conditioning: The R Package ggm

We describe some functions in the R package ggm to derive from a given Markov model, represented by a directed acyclic graph, different types of graphs induced after marginalizing over and conditioning on some of the variables. The package has a few basic functions that find the essential graph, the induced concentration and covariance graphs, and several types of chain graphs implied by the directed acyclic graph (DAG) after grouping and reordering the variables. These functions can be useful to explore the impact of latent variables or of selection effects on a chosen data generating model.

The Algebra of Directed Acyclic Graphs

We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces. Our development provides an initial-algebra semantics for dag structure

A Transition-Based Directed Acyclic Graph Parser for UCCA

We present the first parser for UCCA, a cross-linguistically applicable framework for semantic representation, which builds on extensive typological work and supports rapid annotation. UCCA poses a challenge for existing parsing techniques, as it exhibits reentrancy (resulting in DAG structures), discontinuous structures and non-terminal nodes corresponding to complex semantic units. To our knowledge, the conjunction of these formal properties is not supported by any existing parser. Our transition-based parser, which uses a novel transition set and features based on bidirectional LSTMs, has value not just for UCCA parsing: its ability to handle more general graph structures can inform the development of parsers for other semantic DAG structures, and in languages that frequently use discontinuous structures.Comment: 16 pages; Accepted as long paper at ACL201

Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.Comment: 26 pages, 17 figure