We consider the problem of learning causal information between random
variables in DAGs when allowing arbitrarily many latent and selection
variables. The FCI algorithm (Spirtes et al., 1999) has been explicitly
designed to infer conditional independence and causal information in such
settings. However, FCI is computationally infeasible for large graphs. We
therefore propose a new algorithm, the RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information.
Large contingency tables summarizing categorical variables arise in many
areas. For example in biology when a large number of biomarkers are
cross-tabulated according to their discrete expression level. Interactions of
the variables are generally studied with log-linear models and the structure of
a log-linear model can be visually represented by a graph from which the
conditional independence structure can then be read off.
We consider variable selection in high-dimensional linear models where the
number of covariates greatly exceeds the sample size. We introduce the new
concept of partial faithfulness and use it to infer associations between the
covariates and the response.
We consider variable selection in high-dimensional linear models where the
number of covariates greatly exceeds the sample size. We introduce the new
concept of partial faithfulness and use it to infer associations between the
covariates and the response.
We assume that we have observational data generated from an unknown
underlying directed acyclic graph (DAG) model. A DAG is typically not
identifiable from observational data, but it is possible to consistently
estimate the equivalence class of a DAG. Moreover, for any given DAG, causal
effects can be estimated using intervention calculus. In this paper, we combine
these two parts. For each DAG in the estimated equivalence class, we use
intervention calculus to estimate the causal effects of the covariates on the
response.