The
adaptation algorithm (sequential updating) will update the conditional
probability distribution of a Bayesian belief network in the light of inserted
and propagated evidence (i.e. experience). The adaptation algorithm only applies
to the discrete chance nodes. The algorithm is useful when the graphical
structure and an initial specification of the conditional probability
distributions are present but the modelled domain changes over time, the model
is incomplete, or the model simply does not reflect the modelled domain
properly.
In this section we give a quick overview of sequentially
update the conditional probability tables. It is assumed that the reader is
familiar with the methodology of Bayesian belief networks and influence diagrams
as well as usage of Hugin Runtime (the graphical user interface).
The basic concept of
Bayesian belief is described in basic
concepts section. You can also learn more about influence diagrams in the
same section. To get an introduction to Hugin Runtime refer to A
Small Bayesian Belief Network.
The sequential updating also known as adaptation or sequential
learning makes it possible to update and improve the conditional probability
distribution for a domain as observation are made. Adaptation is especially
useful if the model is incomplete, the modelled domain is drifting over time, or
the model quite simple does not reflect the modelled domain properly. Note that
the graphical structure and an initial specification of conditional probability
distribution must be present prior to adaptation.
The adaptation algorithm implemented in Hugin is developed by
Spiegelhalter and Lauritzen [Spiegelhalter&Lauritzen90].
See also [Cowel&Dawid92]
and [Olesen
et.al.92] for a more detailed mathematical description of the algorithm.
Spiegelhalter and Lauritzen introduced the notion of experience.
The experience is quantitative memory which can be based both on quantitative
expert judgment and past cases. Dissemination of experience refers to the
process of calculating prior conditional distributions for the variables in the
belief network. Retrieval of experience refers to the process of
calculating updated distributions for the parameters that determine the
conditional distributions for the variables in the belief network.
In short the adaptation algorithm will update the conditional
probability distribution of a Bayesian belief network in the light of inserted
and propagated evidence (i.e. experience). Note that adaptation can only be
applied to discrete chance variables.
The experience for a given discrete chance node is
represented as a set of experience counts Alpha0,...,Alphan-1,
where n is the number of configurations of the parents of the node
and Alphai > 0 for all i; Alphai
corresponds to the number of times the parents have been observed to be in the ith
configuration. However, note that the “counts” do not have to be
integers – they can be arbitrary (positive) real number, thus the counts are
only conceptual. The experience counts are stored in a table, experience
table.
When an experience table is created, it is filled with zeros. Since
zero is an invalid experience count, positive values must be stored in the
tables before adaptation can take place. The adaptation algorithm will
only adapt conditional distributions corresponding to parent configurations
having a positive experience count. All other configurations (including all
configurations for nodes with o experience table) are ignored. This convention
can be used to turn on/off adaptation at the levee of individual parent
configurations: setting an experience count to positive number will turn on
adaptation for the associated parent configuration; setting the experience count
to zero or a negative number will turn it off.
Experience tables can be deleted. Note that this will turn off
adaptation for the node associated with the experience table and the initial
conditional distribution will be equal to conditional distribution of the node
at the deletion time.
The
adaptation algorithm also provides an optional fading feature. This
feature reduces the influence of past (and possibly outdated) experience in
order to let the domain model adapt to changing environments. This is achieved
by discounting the experience count Alphai by
a fading factor Deltai, which is a positive real number
less than but typically close to 1. The true fading amount is made proportional
to the probability of the parent configuration in question. to be precise: if
the ith parent given the propagated evidence is pi,
then Alphai is multiplied by (1-pi)+piDeltai)
before adaptation takes place. Note that the experience counts corresponding to
parent configurations that are inconsistent with the propagated evidence (i.e.
configuration with pi = 0) remain unchanged.