Belief change in probabilistic knowledge representations for open and dynamic computing environments
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Date
2020
Authors
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Journal ISSN
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Publisher
University of Zululand
Abstract
Theory refinement in Probabilistic Knowledge Representations is the task of up
dating the Graphical Network structure in light of observations inconsistent with the
current network structure. However, in the literature on Belief Change in Probabilis
tic Knowledge Representations, theory refinement is only thought of as a change in
the model parameters when data consistent with the Network structure is observed.
Such Belief Change is not rich enough to capture the semantics of Belief Change in
dynamic domains. In dynamic domains, the actual network structure at any given
time is unknown and is unobservable. Only the data emitted from the domain is
observable. Further to the foregoing, the Belief Change Model needs to cater to
both changes necessititated by the correction of incorrect Beliefs (Belief Revision)
and changes necessitated by changes in the domain (Belief Update). This thesis hy
pothesised a Belief Change Meta-Model for Bayesian Network (BN) based Knowledge
Representation in dynamic domains, and subsequently used the meta-model to de
fine a Unified Belief Change Model for Bayesian Networks that caters for both Belief
Revision and Belief Update of the Bayesian Network Structure.
The Belief Change Model was conceptualised by first modelling the evolving
Bayesian Network structure as a dynamical system whose impetus for change is driven
by the occurrence of some events in the domain. The derived Unified Belief Change
Model was formally validated by analogy using the Qualitative Belief Change Model
for dynamic environments and the theory of Partially Observable Markov Decision
Processes (POMDP). It was also proven that the proposed Belief Change model meets
the postulates for revision of p-functions.
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Apart from arguing the efficacy of the proposed Unified Belief Change Model from
a theoretical standpoint, this thesis also provides empirical evidence for the same. A
Belief Change operator, the Unified Belief Change Operator for Bayesian Networks
(UBCOBaN), based on the proposed Belief Change Model was developed. The opera
tor was then used to illustrate how the model achieves Belief Change using a synthetic
example with one (1) iteration of Belief Change. Further to the fore-going the operator
was implemented in java and was used for evaluating the efficacy of the model in both
Propositional Bayesian Networks and in Multi-Entity Bayesian Networks (MEBN).
MEBN is a variant of First Order Probabilistic Logic (FOPL) this research chose to
use for evaluating the proposed model for Belief Change in First-Order Probabilis
tic Knowledge Representations. The benchmark propositional Bayesian Networks
used in the study were the ASIA, ALARM, HAILFINDER, HEPAR II, and the AN
DES Bayesian Networks. The benchmark relational datasets considered for MEBN
were the CORA, WebKP, UW std, and Financial std datasets. The results obtained
showed that the proposed model adheres to the principle of minimal change (prin
ciple information economy) better than the classical Search-and-Score algorithm in
all the afore-mentioned propositional Bayesian Networks and all the datasets consid
ered for MEBN. The model was also found to be at least as agile as the classical
Search-and-Score algorithm in instances where data inconsistent with the assumed
network structure was observed. This was observed for all the benchmark proposi
tional Bayesian Networks used in ths study, and all the relational datasets consid
ered for MEBN. The results obtained for an investigation on whether Belief Update
improves rationality of the proposed Unified Belief Change Model on propositional
Bayesian Networks showed that the Unified Belief Change Model with Belief Update
has superior performance compared to the one without Belief Update. However, the
superior performance was not statistically significant at 95% Confidence Interval.
Description
A thesis submitted in fulfillment of the academic requirements for the degree of Doctor of Philosophy in the Department of Computer Science in the Faculty of Science, Agriculture and Engineering, University of Zululand, 2020.
Keywords
Probabilistic Knowledge Representations, Graphical Network, Belief Change