Exact Inference for Continuous-Time Gaussian Process Dynamics
Authors: Katharina Ensinger, Nicholas Tagliapietra , Sebastian Ziesche, Sebastian Trimpe
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Experiments Next, we evaluate our methods numerically and support the intuitive and theoretical findings. Our framework provides the option to train with various integrators of arbitrary order and time irregularity. In contrast to most GP dynamics models, we treat the learned dynamics indeed as an ODE and perform predictions with an integrator that solves the ODE almost exactly. In particular, the prediction integrator does not necessarily correspond to the training integrator. We consider both, mean and DS predictions and conduct experiments with fixed and varying step sizes. We show that (i) for multistep integrators, the higher the order, the better the ODE approximation on regular and irregular grids. (ii) Taylor integrators are especially effective on irregular grids (cf. Sec 3.1). (iii) We can compete with a variational inference baseline. (iv) Through extensive experiments, we investigate which integrator to use in which scenario including their limitations. We further demonstrate that our framework can cope with different choices of integrators. |
| Researcher Affiliation | Collaboration | Katharina Ensinger 1,2 , Nicholas Tagliapietra 1, ,*, Sebastian Ziesche 1, Sebastian Trimpe 2 1 Bosch Center for Artificial Intelligence, Renningen, Germany 2 Institute for Data Science in Mechanical Engineering, RWTH Aachen University |
| Pseudocode | No | The paper does not contain any pseudocode or explicitly labeled algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about providing open-source code for the methodology or a link to a code repository. |
| Open Datasets | Yes | Real spring system: We consider measurements from a linear mass-spring system on an air track from Schmidt and Lipson (2009). ... Human motion data (Mo Cap): Like Hegde et al. (2022), we consider experimental human motion data from CMU Mo Cap database for subject 09 short. |
| Dataset Splits | No | For DHO: "The first 500 steps are used for training, while predictions are performed on the full trajectory." For VDP: "Training is performed on the first 50 steps, predictions are performed on the full trajectory." For Real spring system: "We use the first 400 steps for training, while predictions are performed on the full trajectory." While the paper mentions evaluating error with an adaptive step-size integrator on a "train or validation set" in Section 3.3, specific details, percentages, or absolute counts for a distinct validation split are not provided. |
| Hardware Specification | No | The paper does not provide any specific hardware specifications (e.g., GPU models, CPU types, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions using "ARD kernels" and refers to "Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)" by Rasmussen and Williams (2005) but does not provide specific version numbers for any software libraries, frameworks, or programming languages used. |
| Experiment Setup | Yes | Experimental setup: For all experiments, we consider DS predictions by drawing independent trajectories from the GP posterior and computing the statistical mean and variance. We evaluate the mean squared error (MSE) between data and predictions on five independent runs and report mean and standard deviation. We consider the explicit Euler (AB 1) as a baseline. We further compare to the GP-ODE proposed in Hegde et al. (2022), a variational inference-based approach that works similarly as a neural ODE. By considering orders 1 to 3 for each integrator, we investigate how the order affects the results. All GPs are modeled with ARD kernels (Rasmussen and Williams 2005). We consider simulated systems and real-world data. ... DHO: We consider a timeline with regular step size and generate a trajectory of 10 seconds and step size h = 0.01. ... VDP: We simulate the VDP system (Cveticanin 2013) on an irregular timeline by sampling the step size within a certain range b via ti+1 = ti + h(1 + (w 1/2)b), with w U(0, 1) and step size h = 0.1. Here, we choose b = 0.5. ... We compute rollouts with 100 steps. |