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The Radon dataset is a well-known hierarchical/multilevel dataset. It contains Radon samples from houses in counties across the United States. The goal of the model is to estimate the (log) Radon level in each county based on reading from either the basement or first floor of houses in the county.

The book, which presented this dataset, suggests using either maximum likelihood or Bayesian inference methods to combine data from the various counties, building individual (but dependent) models for each county.

Is there a quantum algorithm that can be applied to this problem?
The features are:

  • floor of Radon measurement: 0 - basement; 1 - first floor
  • county id: a categorical/nominal feature

The label is the logarithm of the Radon level.

Ignoring the county ID and training a single model is trivial, as is training a separate model for each county. I am looking for a mixture model that combines data from all counties to build estimates for each county.

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