In this article, the basic idea of IVGA, i.e., grouping variables according to dependences within the data, was presented and motivated, as well as shown to work in practice. An efficient algorithm was suggested for computing IVGA and shown to work rather well on real data. In the experiments vector quantization (VQ) was used to model the dependences within variable groups. In the calculation of the cost function most of the unknown variables are marginalized out and therefore the cost function can reliably be used for model selection.
One should keep in mind that we used VQ just as a simple example: it could be replaced with any method as long as the necessary cost function is derived for the method. Each variable group could even be modeled using a different method.
The presented approach has implications both for constructing better models of large and complex phenomena and for the efficient computation of such models. However, further research is needed to study these issues in depth.