New framework uses dynamics to justify Gaussian process for turbulent flows.
problem Lack of rigorous justification for Gaussian process priors in turbulent flows.
method Introduces a dynamics-informed Gaussian process framework based on quasi-Gaussianity.
result Provides a principled, long-time dynamical justified GP prior for turbulent flows.
dynoGP uses deep Gaussian processes for dynamic system identification.
problem System identification for complex dynamical systems.
method Interconnecting linear dynamic GPs and static GPs to model dynamic and static nonlinearities.
result Demonstrates effectiveness of the approach using both simulated and real-world data.
New method learns dynamical systems efficiently using active learning.
problem Efficiently learning dynamical systems from data.
method Active learning strategies leveraging Gaussian process regression.
result Data-efficient training of the model through exploratory sampling.
Proposes a Gaussian process model for constrained dynamics learning.
problem Challenges in identifying constrained dynamics of mechanical systems.
method Combines analytical mechanics with Gaussian process regression.
result Improves data efficiency and constraint integrity in predictions.
Modeling interacting objects with latent Gaussian process ODEs.
problem Time uncertainty-aware modeling of continuous-time dynamics of interacting objects.
method A new model using latent Gaussian process ordinary differential equations to infer independent dynamics and interactions.
result Our model improves long-term predictions and successfully encapsulates independent dynamics and interactions.
Ensembles dynamic models using random feature approximations.
problem Online scalable Bayesian learning with dynamic models and ensembling.
method Random feature approximations and dynamic models using random walks.
result Better performance with alternative basis expansions like Hilbert space Gaussian processes.
Proposes DLGPD model to learn dynamics from images for planning.
problem Planning in unknown, indirectly observable environments.
method Deep latent Gaussian process dynamics model trained jointly with neural networks.
result Demonstrates improved data efficiency and transfer learning.
Improved sample efficiency in reinforcement learning with deep Gaussian processes.
problem Efficiently learn to control actions with limited interaction data.
method Deep Gaussian processes that simulate dynamics with depth and prior knowledge.
result Significantly improved early sample efficiency across various tasks, including half-cheetah control.
Gaussian processes for dynamical systems with Koopman equivariance.
problem Forecasting and learning representations of nonlinear dynamical systems.
method Koopman-equivariant Gaussian processes with linear time-invariant responses and trajectory-based equivariance.
result Enhanced forecasting performance compared to kernel-based methods.
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …
New method learns dynamic brain communication patterns across regions.
problem Current methods struggle with time-varying brain communications and scalability.
method Adaptive Delay Model (ADM) using Markovian Gaussian Processes.
result Captures dynamic neural communication patterns over time.
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems
problem Forecasting complex dynamical systems
method Kernel autonomous ODE approach based on Gaussian Processes and Quadratic Order Model Reduction
result Full model outperforms ROM methods in terms of accuracy or computational costs
e-GGPs learn graph vertex transitions over time.
problem Static graph Gaussian Processes cannot handle dynamic graph structures.
method Proposes e-GGPs with a transition function and neighbourhood kernel.
result e-GGPs outperform static GGPs on time-series regression.
New analysis explains pathology of deep Gaussian processes.
problem Pathology of deep Gaussian processes reduces learning capacities with increased layers.
method Study nonlinear dynamic systems corresponding to DGPs, derive recurrence relations.
result Provide tighter bounds and rate of convergence for dynamic systems.
New metrics using Laplace approximation improve Gaussian process model selection.
problem Finding a balance between model accuracy, interpretability, and simplicity.
method Introducing multiple metrics based on the Laplace approximation to evaluate Gaussian process models.
result Our metrics provide comparable performance to dynamic nested sampling but are significantly faster.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often ill-conditioned: the observations can be noisy, not assuming the luxury of relative…
Extends DRFGP to make GPs more robust and adaptive for dynamic, noisy data.
problem Limited scalability, static targets, and brittleness to outliers in GPs.
method Introduces robust-filtering update and dynamic adaptation mechanism.
result Enhanced stability and accuracy in modeling dynamic, noisy data.
Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.
problem Understanding convergence of neural networks to Gaussian processes during training.
method Explicit upper bounds on quadratic Wasserstein distance between trained networks and Gaussian approximations.
result Polynomial decay of approximation error with network width and training time.
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the v…
Textual network embedding aims to learn low-dimensional representations of text-annotated nodes in a graph. Prior work in this area has typically focused on fixed graph structures; however, real-world networks are often dynamic. We address this challenge with a novel end-to-end node-embedding model, called Dynamic Embe…
We develop a new DTSM with nonlinearities using Gaussian Processes for better interest rate forecasting.
problem Linear DTSMs fail to capture nonlinear relationships between macroeconomic variables and interest rates.
method We propose a Gaussian Process-based sequential Monte Carlo estimation and forecasting scheme.
result Nonlinear models outperform linear ones in forecasting core inflation, leading to significant economic value gains.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.
Active learning selects inputs for GPSSM to learn latent states.
problem Optimally learn latent states of a GPSSM through active selection of inputs.
method Use mutual information to select informative inputs; approximate mutual information for GPSSM.
result Effective active learning of GPSSM dynamics in physical systems.
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to …
The paper addresses GP dynamics by improving simulation and prediction accuracy.
problem GP dynamics often underestimate prediction uncertainty, leading to safety issues.
method The paper introduces sampling-based and linearization-based techniques to account for the correlation between successive function evaluations.
result The proposed methods provide more accurate trajectory distributions and prediction uncertainties.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
Gaussian processes are conditioned on various types of data.
problem Exact inference in Gaussian processes is limited to linear-Gaussian settings.
method Established an equivalence between GPs and linear diffusion models, allowing for approximate inference in non-linear settings.
result A general-purpose GP inference scheme that handles various conditioning statements, including non-linear physics and natural language.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attr…
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is controlled by a shared global latent process and a private local latent process…
MAGI-X learns unknown dynamics from data without numerical integration.
problem Difficult to propose ODEs in closed-form for complex systems.
method MAGI-X uses neural networks within a manifold-constrained Gaussian process framework.
result MAGI-X achieves competitive accuracy in fitting and forecasting with reduced computational time.
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computationa…
We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian processes is the warping of inputs through infinitely deep, but infinitesimal, diff…
This work compares data reduction criteria for online Gaussian Processes.
problem The computational complexity of Gaussian Processes limits their applicability to small datasets and streaming scenarios.
method Unified comparison of several data reduction criteria, analyzing computational complexity and reduction behavior.
result Practical guidelines for choosing a suitable data reduction criterion for online Gaussian Processes.
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
DKL combines neural networks and Gaussian processes but can overfit.
problem Overfitting in DKL models.
method Careful experimentation on various datasets and investigation of optimization dynamics.
result Overfitting from DKL can be worse than non-Bayesian models.
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…
The paper proposes a GP-based method for discovering second-order particle dynamics models.
problem Discovering a general second-order particle-based model for agent interactions.
method Gaussian Process-based approach integrating two independent GP priors on latent interaction kernels.
result The method learns effective nonlinear dynamics representations from small data sets.
GP-NODE combines Gaussian processes and NeuralODEs for Bayesian system identification.
problem Bayesian systems identification from partial, noisy and irregular observations.
method Differentiable programming, Hamiltonian Monte Carlo, Gaussian Process priors, sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Proposes a flexible MGP model for dynamic, sparse correlations.
problem Handling dynamic and sparse correlations in multivariate data.
method Non-stationary MGP with dynamic spike-and-slab prior and EM algorithm.
result Captures dynamic and sparse correlations effectively.
This paper introduces a multi-output Gaussian process for censored data.
problem Modeling bias in censored data using correlations between multiple outputs.
method Heteroscedastic multi-output Gaussian process with input-dependent noise and variational inference.
result The model better estimates the true process under complex censoring dynamics.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.