# Parametric Learning - Adaptation

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. The fading for a given discrete chance node is stored in a table namely fading table, where each value in the table corresponds to a parent configuration. The fading factor Deltai can be set to 1: this implies that cases are accumulated (that is, no fading takes place). Setting Deltai to a value greater than 1 or less than or equal to 0 will disable adaptation for the ith parent configuration (just as setting Alphai to an invalid value will).

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