Mixture Models from Multiresolution 0-1 Data

Multiresolution data has received considerable research interest due to the practical usefulness in combining datasets in different resolutions into a single analysis. Most models and methods can only model a single data resolution, that is, vectors of the same dimensionality, at a time. This is also true for mixture models, the model of interest. In this paper, we propose a multiresolution mixture model capable of modeling data in multiple resolutions. Firstly, we define the multiresolution component distributions of mixture models from the domain ontology. We then learn the parameters of the component distributions in the Bayesian network framework. Secondly, we map the multiresolution data in a Bayesian network setting to a vector representation to learn the mixture coefficients and the parameters of the component distributions. We investigate our proposed algorithms on two data sets. A simulated data allows us to have full data observations in all resolutions. However, this is unrealistic in all practical applications. The second data consists of DNA aberrations data in two resolutions. The results with multiresolution models show improvement in modeling performance with regards to the likelihood over single resolution mixture models.