Abstract
Uncertainty quantification has been a core of the statistical machine
learning, but its computational bottleneck has been a serious challenge for
both Bayesians and frequentists. We propose a model-based framework in
quantifying uncertainty, called predictive-matching Generative Parameter
Sampler (GPS). This procedure considers an Uncertainty Quantification (UQ)
distribution on the targeted parameter, which matches the corresponding
predictive distribution to the observed data. This framework adopts a
hierarchical modeling perspective such that each observation is modeled by an
individual parameter. This individual parameterization permits the resulting
inference to be computationally scalable and robust to outliers. Our approach
is illustrated for linear models, Poisson processes, and deep neural networks
for classification. The results show that the GPS is successful in providing
uncertainty quantification as well as additional flexibility beyond what is
allowed by classical statistical procedures under the postulated statistical
models.
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