On Causal Compositional Models: Simple Examples

Jiroušek, Radim

doi:10.1007/978-3-319-08795-5_53

Cited by 6 publications

(5 citation statements)

References 4 publications

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“…We have described causal compositional models, originally introduced in [8] in the probabilistic framework, in the VBS framework. We have shown that both conditioning and interventions can easily be described using the composition operator.…”

Section: Discussionmentioning

confidence: 99%

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Causal compositional models in valuation-based systems with examples in specific theories

Jirouek

Shenoy

2016

International Journal of Approximate Reasoning

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We show that Pearl's causal networks can be described using causal compositional models (CCMs) in the valuationbased systems (VBS) framework. One major advantage of using the VBS framework is that as VBS is a generalization of several uncertainty theories (e.g., probability theory, a version of possibility theory where combination is the product t-norm, Spohn's epistemic belief theory, and Dempster-Shafer belief function theory), CCMs, initially described in probability theory, are now described in all uncertainty calculi that fit in the VBS framework. We describe conditioning and interventions in CCMs. Another advantage of using CCMs in the VBS framework is that both conditioning and intervention can be easily described in an elegant and unifying algebraic way for the same CCM without having to do any graphical manipulations of the causal network. We describe how conditioning and intervention can be computed for a simple example with a hidden (unobservable) variable. Also, we illustrate the algebraic results using numerical examples in some of the specific uncertainty calculi mentioned above.

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Section: Discussionmentioning

confidence: 99%

“…In [8], causal probabilistic models, which are graphical probability models, were described by causal compositional models, which are algebraic probability models. Compositional models are based on the idea that a multidimensional probability model can be assembled, i.e., composed, from a collection of its lower-dimensional marginals.…”

Section: Introductionmentioning

confidence: 99%

Causal compositional models in valuation-based systems with examples in specific theories

Jirouek

Shenoy

2016

International Journal of Approximate Reasoning

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“…Compositional models were introduced to construct probability distributions from lowerorder probability distributions [6,8,9,11,13] as an operational alternative to the graphical approach used to model Bayesian and causal networks. They were also applied to belief functions [10,15,16], possibility functions [15] and Shenoy valuations [14].…”

Section: Introductionmentioning

confidence: 99%

Marginalization in models generated by compositional expressions

Malvestuto¹

2015

Kybernetika

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“…In contrast to this common approach, in this paper we take advantage of the algebraic apparatus of compositional models [3]. In fact, this paper is a continuation of the contribution to IPMU 2014 conference [4], where the first ideas on causal compositional models were published. The present paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%