Variable selection via additive conditional independence

Conditional Independence Models via Filtrations

We formulate a novel approach to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, our objective is to place informative prior distributions over decomposable graphs and sample efficiently from the induced posterior distribution. The key idea we develop in this paper is a parametrization of decomposable hypergraphs using the geometry of poin...

Testing Conditional Independence via Empirical Likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis an...

Propositional Independence Conditional independence

Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and proper...

Variable Selection in Nonparametric Additive Models.

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expan...

Conditional Independence