Version: 1.0.0

Pattern language family: BN

Modeling phase:

2. The conceptualization phase of a system of interest
3. The technical implementation

Modeling step:

6. Choice of estimation performance criteria and technique
7. Identification of model structure and parameters' values

Problem:

Introducing new variables to the network, as a result of applying parent divorcing, or if some variables’ data have never been observed means that these variables will cut the influence path between the input nodes and the output nodes. Particularly in the case when the new nodes are introduced through parent divorcing, these new nodes don’t necessarily represent a real variable that we can acquire data for, hence determine its possible states.

Solution:

Apply statistical methods that can condense a group of observed variables into a smaller group of latent variables. One of the methods that can be used for this purpose is Factor analysis (FA), which can describe the relation between a set of observed variables in terms of a smaller number of unobserved variables. In the case of latent variables in a BN, each of them will be represented as an index that reflects the performance of its parent variables. The following steps can be followed to apply FA in a BN context:

  • Determine the set of unparameterized parents for each latent variable.

  • In order to proceed with FA, we need to choose the number of factors to keep, so a suitable solution is to choose number of factors = number of parents -1.

  • Perform factorial axes rotation using a rotation algorithm, e.g. Varimax rotation.

  • Factor loadings are then used to give weights to parameters. The weights represent the proportion of total unit variance of the parameter that is explained by the factor.

  • Associate weights to parameters based on the ratio between the variance explained by the parameter to the total explained variable.

  • Finally, the weights are used to aggregate the parents’ data to assign a new value for the latent variable.

Applying this solution will result in new parameters will be acquired for the latent variables added to the network so they can be discretized and used for inference.

Structure: NA

Constraints:

This solution works under the following conditions:

  • This solution can be applied if the parents of the latent variable are continues.

  • The resulting parameters for the latent variable will be continues and will need to be discretized.

Related patterns:

Design choice and model quality:

  • 2.R
  • 4.U

Resources:

  • Holmes, D. E. (Ed.). (2008). Innovations in Bayesian networks: theory and applications (Vol. 156). Springer.

  • Marcot, B. G. (2017). Common quandaries and their practical solutions in Bayesian network modeling. Ecological Modelling, 358, 1-9.

  • Yong, A. G., & Pearce, S. (2013). A beginner’s guide to factor analysis: Focusing on exploratory factor analysis. Tutorials in quantitative methods for psychology, 9(2), 79-94.

  • Tripathi, M., & Singal, S. K. (2019). Allocation of weights using factor analysis for development of a novel water quality index. Ecotoxicology and environmental safety, 183, 109510.

  • Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffman, A. and Giovannini, E. (2006), Handbook on constructing composite indicators: Methodology and user guide OECD, Statistics Working Paper 158.