Probabilistic Argumentation and Information Algebras of Probability Potentials on Families of Compatible Frames

10/08/2018
by   Juerg Kohlas, et al.
0

Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate models based on families of variables. The crucial relation of conditional independence between frames of a f.c.f is introduced and shown to form a quasi-separoid, a weakening of the well-known structure of a separoid. It is shown that PAS generate probability potentials on the frames of the f.c.f. The operations of aggregating different PAS and of transport of a PAS from one frame to another induce an algebraic structure on the family of potentials on the f.c.f, an algebraic structure which is similar to valuation algebras related to Bayesian networks, but more general. As a consequence the well-known local computation architectures of Bayesian networks for inference apply also for the potentials on f.c.f. Conditioning and conditionals can be defined for potentials and it is shown that these concepts satisfy similar properties as conditional probability distributions. Finally a max/prod algebra between potentials is defined and applied to find most probable configurations for a factorization of potentials.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/27/2014

Conditional Plausibility Measures and Bayesian Networks

A general notion of algebraic conditional plausibility measures is defin...
research
01/30/2013

Lazy Propagation in Junction Trees

The efficiency of algorithms using secondary structures for probabilisti...
research
07/23/2012

Probability Bracket Notation, Multivariable Systems and Static Bayesian Networks

Probability Bracket Notation (PBN) is applied to systems of multiple ran...
research
07/11/2012

A New Characterization of Probabilities in Bayesian Networks

We characterize probabilities in Bayesian networks in terms of algebraic...
research
01/13/2019

Bayesian Networks for Max-linear Models

We study Bayesian networks based on max-linear structural equations as i...
research
06/29/2018

Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks

The paper extends Bayesian networks (BNs) by a mechanism for dynamic cha...
research
12/12/2012

Exploiting Functional Dependence in Bayesian Network Inference

We propose an efficient method for Bayesian network inference in models ...

Please sign up or login with your details

Forgot password? Click here to reset