# Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networks

arXiv: https://arxiv.org/abs/2305.17063 · HTML: https://mlsanity.com/paper/2305.17063/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 56 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Joint Face Detection and Alignment using Multi-task Cascaded Convolutional Networks](https://mlsanity.com/paper/1604.02878/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [Moving Window Regression: A Novel Approach to Ordinal Regression](https://mlsanity.com/paper/2203.13122/) (2022)
- [BridgeNet: A Continuity-Aware Probabilistic Network for Age Estimation](https://mlsanity.com/paper/1904.03358/) (2019)
- [Nested Kriging predictions for datasets with large number of observations](https://mlsanity.com/paper/1607.05432/) (2016)
- [Scaled Vecchia approximation for fast computer-model emulation](https://mlsanity.com/paper/2005.00386/) (2020)
- [Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference](https://mlsanity.com/paper/2112.14591/) (2021)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)

## Built on by (most cited first, 3 of 3)

- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning](https://mlsanity.com/paper/2606.17513/) (2026)
- [Practical Deep Heteroskedastic Regression](https://mlsanity.com/paper/2603.01750/) (2026)

## Abstract (arXiv)

For regression tasks, standard Gaussian processes (GPs) provide natural uncertainty quantification (UQ), while deep neural networks (DNNs) excel at representation learning. Deterministic UQ methods for neural networks have successfully combined the two and require only a single pass through the neural network. However, current methods necessitate changes to network training to address feature collapse, where unique inputs map to identical feature vectors. We propose an alternative solution, the deep Vecchia ensemble (DVE), which allows deterministic UQ to work in the presence of feature collapse, negating the need for network retraining. DVE comprises an ensemble of GPs built on hidden-layer outputs of a DNN, achieving scalability via Vecchia approximations that leverage nearest-neighbor conditional independence. DVE is compatible with pretrained networks and incurs low computational overhead. We demonstrate DVE's utility on several datasets and carry out experiments to understand the inner workings of the proposed method.