mlsanityData to 7 Oct 2026

Trust Your Robots! Predictive Uncertainty Estimation of Neural Networks with Sparse Gaussian Processes

arXiv 2109.09690 ↗First posted 20 Sep 2021cs.RO cs.AI cs.CVcited by 12

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Abstract (arXiv)

This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse Gaussian Processes (GPs). We prove theoretically that DNNs can be seen as a special case of sparse GPs, namely mixtures of GP experts (MoE-GP), and we devise a learning algorithm that brings the derived theory into practice. In experiments from two different robotic tasks -- inverse dynamics of a manipulator and object detection on a micro-aerial vehicle (MAV) -- we show the effectiveness of our approach in terms of predictive uncertainty, improved scalability, and run-time efficiency on a Jetson TX2. We thus argue that our approach can pave the way towards reliable and fast robot learning systems with uncertainty awareness.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 33 of its 62 references that are in the map. First posted on arXiv 20 Sep 2021.

Builds on

33 of 62 references.

References · 33

  1. 2020End-to-End Object Detection with Transformerscited by 7,384
  2. 2017On Calibration of Modern Neural Networkscited by 4,860
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  6. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  7. 2018Evidential Deep Learning to Quantify Classification Uncertaintycited by 728
  8. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
  9. 2017Deep Neural Networks as Gaussian Processescited by 617
  10. 2015Deep Kernel Learningcited by 440
  11. 2018When Gaussian Process Meets Big Data: A Review of Scalable GPscited by 205
  12. 2019A General Framework for Uncertainty Estimation in Deep Learningcited by 119
21 more
  1. 2020Bayesian Deep Ensembles via the Neural Tangent Kernelcited by 90
  2. 2019Approximate Inference Turns Deep Networks into Gaussian Processescited by 89
  3. 2019'In-Between' Uncertainty in Bayesian Neural Networkscited by 79
  4. 2019Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagationcited by 74
  5. 2019Identifying Unknown Instances for Autonomous Drivingcited by 73
  6. 2019BayesOD: A Bayesian Approach for Uncertainty Estimation in Deep Object Detectorscited by 68
  7. 2017Hard Mixtures of Experts for Large Scale Weakly Supervised Visioncited by 67
  8. 2019Non-Parametric Calibration for Classificationcited by 57
  9. 2018Constant-Time Predictive Distributions for Gaussian Processescited by 48
  10. 2021Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networkscited by 32
  11. 2019Benchmarking the Neural Linear Model for Regressioncited by 31
  12. 2020Estimating Model Uncertainty of Neural Networks in Sparse Information Formcited by 31
  13. 2017Failing to Learn: Autonomously Identifying Perception Failures for Self-driving Carscited by 28
  14. 2020Learning to Localize in New Environments from Synthetic Training Datacited by 21
  15. 2016Introspective Perception: Learning to Predict Failures in Vision Systemscited by 17
  16. 2020Scalable Uncertainty for Computer Vision with Functional Variational Inferencecited by 12
  17. 2020Exploring the Uncertainty Properties of Neural Networks' Implicit Priors in the Infinite-Width Limitcited by 12
  18. 2017Patchwork Kriging for Large-scale Gaussian Process Regressioncited by 9
  19. 2020Bayesian Optimization Meets Laplace Approximation for Robotic Introspectioncited by 6
  20. 2020Visual-Inertial Telepresence for Aerial Manipulationcited by 4
  21. 2020Learning Multiplicative Interactions with Bayesian Neural Networks for Visual-Inertial Odometrycited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 5; 2024: 2; 2025: 1; 2026: 1.

12 papers.

  1. 2022Interpretable Self-Aware Neural Networks for Robust Trajectory Predictioncited by 22
  2. 2023Variational Linearized Laplace Approximation for Bayesian Deep Learningcited by 17
  3. 2024Evaluating Uncertainty-based Failure Detection for Closed-Loop LLM Plannerscited by 15
  4. 2021Bayesian Active Learning for Sim-to-Real Robotic Perceptioncited by 8
  5. 2023Sparse Variational Student-t Processescited by 8
  6. 2023Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learningcited by 7
  7. 2023Learning Expressive Priors for Generalization and Uncertainty Estimation in Neural Networkscited by 4
  8. 2024Sparse Variational Student-t Processes for Heavy-tailed Modelingcited by 2
  9. 2025A Critical Synthesis of Uncertainty Quantification and Foundation Models in Monocular Depth Estimationcited by 2
  10. 2022Virtual Reality via Object Pose Estimation and Active Learning: Realizing Telepresence Robots with Aerial Manipulation Capabilitiescited by 1
  11. 2023SemiGPC: Distribution-Aware Label Refinement for Imbalanced Semi-Supervised Learning Using Gaussian Processescited by 0
  12. 2026SPIRIT: Perceptive Shared Autonomy for Robust Robotic Manipulation under Deep Learning Uncertaintycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2019Uncertainty Aware Learning from Demonstrations in Multiple Contexts using Bayesian Neural Networks
  2. 2023Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification
  3. 2020Fast Deep Mixtures of Gaussian Process Experts
  4. 2024Deep Gaussian Covariance Network with Trajectory Sampling for Data-Efficient Policy Search
  5. 2025ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling
  6. 2022dPMP-Deep Probabilistic Motion Planning: A use case in Strawberry Picking Robot
  7. 2025Bayesian Inverse Physics for Neuro-Symbolic Robot Learning
  8. 2025UF-RNN: Real-Time Adaptive Motion Generation Using Uncertainty-Driven Foresight Prediction