Sparse Nested Markov models with Log-linear Parameters
This work addresses the need for efficient modeling with hidden variables in statistics, machine learning, and causal inference, representing an incremental improvement by adapting sparsity methods to nested Markov models.
The paper tackles the problem of making nested Markov models practical for modeling and inference by limiting the number of parameters while capturing constraints from DAG marginals, and it introduces a log-linear parameterization that enables sparse modeling, with advantages demonstrated in a simulation study.
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which captures equality constraints found in marginals of directed acyclic graph (DAG) models. Some of these constraints, such as the so called `Verma constraint', strictly generalize conditional independence. To make modeling and inference with nested Markov models practical, it is necessary to limit the number of parameters in the model, while still correctly capturing the constraints in the marginal of a DAG model. Placing such limits is similar in spirit to sparsity methods for undirected graphical models, and regression models. In this paper, we give a log-linear parameterization which allows sparse modeling with nested Markov models. We illustrate the advantages of this parameterization with a simulation study.