# Rapid Risk Minimization with Bayesian Models Through Deep Learning Approximation

arXiv: https://arxiv.org/abs/2103.15682 · HTML: https://mlsanity.com/paper/2103.15682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 51 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Neural Network with Unbounded Activation Functions is Universal Approximator](https://mlsanity.com/paper/1505.03654/) (2015)
- [A Bayesian Data Augmentation Approach for Learning Deep Models](https://mlsanity.com/paper/1710.10564/) (2017)
- [Dropout-based Active Learning for Regression](https://mlsanity.com/paper/1806.09856/) (2018)
- [Using Deep Neural Network Approximate Bayesian Network](https://mlsanity.com/paper/1801.00282/) (2017)

## Abstract (arXiv)

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with the speed of a NN. For a BM, making predictions with the lowest expected loss requires integrating over the posterior distribution. When exact inference of the posterior predictive distribution is intractable, approximation methods are typically applied, e.g. Monte Carlo (MC) simulation. For MC, the variance of the estimator decreases with the number of samples - but at the expense of increased computational cost. Our approach removes the need for iterative MC simulation on the CPU at prediction time. In brief, it works by fitting a NN to synthetic data generated using the BM. In a single feed-forward pass, the NN gives a set of point-wise approximations to the BM's posterior predictive distribution for a given observation. We achieve risk minimized predictions significantly faster than standard methods with a negligible loss on the test dataset. We combine this approach with Active Learning to minimize the amount of data required for fitting the NN. This is done by iteratively labeling more data in regions with high predictive uncertainty of the NN.