Population-aware Hierarchical Bayesian Domain Adaptation via Multiple-component Invariant Learning
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Observational transport relates to transferring a statistical relation R(P) from environment (π) characterized by probability distribution P and causal diagram G to another environment (π^*) characterized by P^*, G^*. In doing so it is expected that the causal mechanism is known a priori and the relation to be transferred is learned from both the source environment consisting of variables V and the target environment comprised of variables V^*. The causal diagram helps to identify what part of the statistical relation R(P) (invariant information) is transportable from the source environment (π) while also identifying the target environment (π^*) specific relation R(P^*) which is learned empirically from the available data. While domain adaptation is a common technique to learn the invariant information across the entire population (dataset), in health care/consumer transactions there is invariant information based on population subgroups. A further issue is that all subgroups are not equally represented across the different environments resulting into selection bias. We posit that we can combine the environment and population invariant information in a novel multi-component population-aware hierarchical domain adaptation Bayesian framework in the presence of the selection bias. We also study the conditions under which invariant learning fails; leading to reliance on the environment-specific attributes. Experimental results on real-world data for influenza prediction show the model can improve prediction in the case of largely unlabelled target data by harnessing both domain and population invariant information, with implications for human-generated data, fair algorithms and human well-being.
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