# Nonparametric learning from Bayesian models with randomized objective functions

arXiv: https://arxiv.org/abs/1806.11544 · HTML: https://mlsanity.com/paper/1806.11544/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 17 of 17)

- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Posterior Uncertainty Quantification in Neural Networks using Data Augmentation](https://mlsanity.com/paper/2403.12729/) (2024)
- [On the Properties and Estimation of Pointwise Mutual Information Profiles](https://mlsanity.com/paper/2310.10240/) (2023)
- [Enhancing Transfer Learning with Flexible Nonparametric Posterior Sampling](https://mlsanity.com/paper/2403.07282/) (2024)
- [Bayesian Quantification with Black-Box Estimators](https://mlsanity.com/paper/2302.09159/) (2023)
- [A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks](https://mlsanity.com/paper/2303.02637/) (2023)
- [Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Cases](https://mlsanity.com/paper/2306.01468/) (2023)
- [Reproducible Parameter Inference Using Bagged Posteriors](https://mlsanity.com/paper/2311.02019/) (2023)
- [Generative vs. Discriminative modeling under the lens of uncertainty quantification](https://mlsanity.com/paper/2406.09172/) (2024)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancy](https://mlsanity.com/paper/2308.14048/) (2023)
- [Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization](https://mlsanity.com/paper/2401.15771/) (2024)
- [Nonparametric posterior learning for emission tomography with multimodal data](https://mlsanity.com/paper/2108.00866/) (2021)
- [Predictive Coresets](https://mlsanity.com/paper/2502.05725/) (2025)
- [A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimation](https://mlsanity.com/paper/2503.08902/) (2025)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)
- [Variational predictive resampling](https://mlsanity.com/paper/2605.11168/) (2026)

## Abstract (arXiv)

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian nonparametric approach to learning that makes use of statistical models, but does not assume that the model is true. Our approach has provably better properties than using a parametric model and admits a Monte Carlo sampling scheme that can afford massive scalability on modern computer architectures. The model-based aspect of learning is particularly attractive for regularizing nonparametric inference when the sample size is small, and also for correcting approximate approaches such as variational Bayes (VB). We demonstrate the approach on a number of examples including VB classifiers and Bayesian random forests.