Conditional and unconditional statistical independence

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...

Conditional independence, conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law...

From Conditional to Unconditional Rewriting

An automated technique to translate conditional rewrite rules into unconditional ones is presented, which is suitable to implement, or compile, conditional rewriting on top of much simpler and easier to optimize unconditional rewrite systems. An experiment performed on world’s fastest conditional rewriting engines shows that speedups for conditional rewriting of an order of magnitude can alread...

Eliciting conditional and unconditional rank correlations from conditional probabilities

Causes of uncertainties may be interrelated and may introduce dependencies. Ignoring these dependencies may lead to large errors. A number of graphical models in probability theory such as dependence trees, vines and (continuous) Bayesian belief nets [Cooke RM. Markov and entropy properties of tree and vine-dependent variables. In: Proceedings of the ASA section on Bayesian statistical science,...

Conditional Independence