Conditional Probability Distributions (CPD) are typically represented by Conditional Probability Tables (CPT), in which there is one probability distribution for each combination of the states of the parent nodes.
Even though in BayesiaLab the final internal model is in the form of a CPT, the definition of the CPD can be facilitated by using the Deterministic or Equation modes in the Node Editor.
BayesiaLab 5.3 now offers the ability of using Conditional Probability Trees (CPTr) for compactly representing CPDs by exploiting Contextual Independencies, e.g. when the state of one parent makes the other co-parent(s) independent of the child node.
CPTr are available in the Node Editor, so you can manually specify a Tree. Also, they are now integrated in BayesiaLab's machine learning algorithms:
- For estimating the parameters of a given network: this allows generalizing probability distributions, either if data is scarce for some combination of parents' states, or if the distributions are not significantly different.
- For estimating the parameters and learning the structure of a graph: this returns a more complex structure as adding parents with CPTr can be less costly than with CPT.
New Feature: Tree Mode in Node Editor
Node Editor | Probability Distribution | Tree
New Feature: Parameter Estimation with Trees
Edit | Parameter Estimation with Trees
If this option is checked, the parameters will no longer be estimated using the Maximum Likelihood Estimation for each combination of states. Rather, they will be estimated by machine learning a probabilistic tree that exploits any regularities in the data. This has the objective of compactly representing the relationship between the parent and child nodes.
- We define the MDL score (Minimum Description Length) as a measure of the quality of candidate trees with respect to the available data. This score, which is derived from Information Theory, automatically takes into account the data likelihood with respect to the tree and its structural complexity.
- Trees are available for Parameter Learning, Unsupervised Structural Learning (Taboo and Taboo Order only) and Supervised Learning.
- The Structural Coefficient and Local Structural Coefficients used for computing the MDL score of a Bayesian networks are also used for computing the MDL score of Trees.
- In this context, the Smoothing Parameter is also taken into account.
- If no regularities can be exploited, tables are used as usual.
If the (conditional) dependency of a parent with its child is not strong enough, that parent will not be included in the induced tree.
Even if the link is not physically removed, it is "soft-deleted" through the parameters.
In this example, Evoque Joy is not dependent on Flowery given Fresh.
Nodes with CPTr are displayed in pink.
Such nodes can be selected by using Edit | Select Nodes | Generalized
Whenever Trees are used instead of Tables, an icon is added in the lower right corner of the graph window: