Equivalence of compositional expressions and independence relations in compositional models

Title:

Equivalence of compositional expressions and independence relations in compositional models

Creator:

Malvestuto, Francesco M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:83e9784d-a6fd-4156-8470-7f7399c912f9
uuid:83e9784d-a6fd-4156-8470-7f7399c912f9

Subject:

compositional expression, compositional model, running intersection property, and perfect sequence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We generalize Jiroušek's (\emph {right}) \emph {composition operator} in such a way that it can be applied to distribution functions with values in a "semifield", and introduce (parenthesized) \emph {compositional expressions}, which in some sense generalize Jiroušek's "generating sequences" of compositional models. We say that two compositional expressions are \emph {equivalent} if their evaluations always produce the same results whenever they are defined. Our first result is that a set system H is star-like with centre X \emph {if and only if} every two compositional expressions with "base scheme" H and "key" X are equivalent. This result is stronger than Jiroušek's result which states that, if H is star-like with centre X, then every two generating sequences with base scheme H and key X are equivalent. Then, we focus on \emph {canonical expressions}, by which we mean compositional expressions θ such that the sequence of the sets featured in θ and arranged in order of appearance enjoys the "running intersection property". Since every compositional expression, whose base scheme is a star-like set system with centre X and whose key is X, is a canonical expression, we investigate the equivalence between two canonical expressions with the same base scheme and the same key. We state a graphical characterization of those set systems H such that every two canonical expressions with base scheme H and key X are equivalent, and also provide a graphical algorithm for their recognition. Finally, we discuss the problem of detecting conditional independences that hold in a compositional model.d

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[322]-362

Source:

Kybernetika | 2014 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false