# Generative Parameter Sampler For Scalable Uncertainty Quantification

## TL;DR

This paper introduces the Generative Parameter Sampler (GPS), a scalable and robust framework for uncertainty quantification that matches predictive distributions to observed data across various models.

## Contribution

The paper presents a novel hierarchical, model-based approach called GPS that improves scalability and robustness in uncertainty quantification for complex models.

## Key findings

- GPS provides accurate uncertainty estimates in linear models.
- GPS demonstrates robustness to outliers in various settings.
- The method is effective for deep neural network classification.

## 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.