# Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models

arXiv: https://arxiv.org/abs/2309.06655 · HTML: https://mlsanity.com/paper/2309.06655/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 28 of 28)

- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Sample-Efficient Safety Assurances using Conformal Prediction](https://mlsanity.com/paper/2109.14082/) (2021)
- [Out-of-Distribution Detection for Automotive Perception](https://mlsanity.com/paper/2011.01413/) (2020)
- [A System-Level View on Out-of-Distribution Data in Robotics](https://mlsanity.com/paper/2212.14020/) (2022)
- [Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks](https://mlsanity.com/paper/2102.12567/) (2021)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Actively Learning Gaussian Process Dynamics](https://mlsanity.com/paper/1911.09946/) (2019)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Failure Prediction with Statistical Guarantees for Vision-Based Robot Control](https://mlsanity.com/paper/2202.05894/) (2022)
- [Computationally Efficient Bayesian Learning of Gaussian Process State Space Models](https://mlsanity.com/paper/1506.02267/) (2015)
- [A flexible state space model for learning nonlinear dynamical systems](https://mlsanity.com/paper/1603.05486/) (2016)
- [Multi-Agent Safe Planning with Gaussian Processes](https://mlsanity.com/paper/2008.04452/) (2020)
- [Generative Causal Representation Learning for Out-of-Distribution Motion Forecasting](https://mlsanity.com/paper/2302.08635/) (2023)
- [The Value of Out-of-Distribution Data](https://mlsanity.com/paper/2208.10967/) (2022)
- [On the Design of LQR Kernels for Efficient Controller Learning](https://mlsanity.com/paper/1709.07089/) (2017)
- [Safety-Critical Control with Bounded Inputs via Reduced Order Models](https://mlsanity.com/paper/2303.03247/) (2023)
- [Nonlinear State Space Model Identification Using a Regularized Basis Function Expansion](https://mlsanity.com/paper/1510.00563/) (2015)

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

- [Unpacking Failure Modes of Generative Policies: Runtime Monitoring of Consistency and Progress](https://mlsanity.com/paper/2410.04640/) (2024)
- [General OOD Detection via Model-aware and Subspace-aware Variable Priority](https://mlsanity.com/paper/2512.13003/) (2025)
- [Kernel-Based Metrics Learning for Uncertain Opponent Vehicle Trajectory Prediction in Autonomous Racing](https://mlsanity.com/paper/2609.17147/) (2026)

## Abstract (arXiv)

In order for robots to safely navigate in unseen scenarios using learning-based methods, it is important to accurately detect out-of-training-distribution (OoD) situations online. Recently, Gaussian process state-space models (GPSSMs) have proven useful to discriminate unexpected observations by comparing them against probabilistic predictions. However, the capability for the model to correctly distinguish between in- and out-of-training distribution observations hinges on the accuracy of these predictions, primarily affected by the class of functions the GPSSM kernel can represent. In this paper, we propose (i) a novel approach to embed existing domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on receding-horizon predictions. Domain knowledge is provided in the form of a dataset, collected either in simulation or by using a nominal model. Numerical results show that the informed kernel yields better regression quality with smaller datasets, as compared to standard kernel choices. We demonstrate the effectiveness of the OoD monitor on a real quadruped navigating an indoor setting, which reliably classifies previously unseen terrains.