Multi-output Gaussian processes have received increasing attention during the last few years as a natural mechanism to extend the powerful flexibility of Gaussian processes to the setup of multiple output variables. The key point here is the ability to design kernel functions that allow exploiting the correlations betw…
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48 results for “Gaussian Process Latent Force Model”
Fast Kernel Approximations for Latent Force Models and Convolved Multiple-Output Gaussian processesstat.ML
A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classica…
A Gaussian process latent force model for joint input-state estimation in linear structural systemscs.LG
The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force mo…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model complexity, or a full specification is hard to motivate. Latent force models achieve …
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
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.
Study uses GPLFM to create Digital Twin for ferry quay health monitoring.
problem Deterioration of ferry quays due to harsh maritime environments and impacts.
method Gaussian Process Latent Force Model (GPLFM) integrating physics-based model and machine learning.
result GPLFM provides accurate acceleration response estimates, even under simplifying assumptions.
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the ex…
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …
Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modellingcs.LG
A scalable GPVAE method using local adjacencies to approximate GP inference.
problem Scalability issues in exact GP inference for large-scale GPVAEs.
method Neighbour-driven approximation strategy that confines computations to nearest neighbours.
result Outperforms other GPVAE variants in predictive performance and computational efficiency.
Multi-output Gaussian processes (GPs) are a flexible Bayesian nonparametric framework that has proven useful in jointly modeling the physiological states of patients in medical time series data. However, capturing the short-term effects of drugs and therapeutic interventions on patient physiological state remains chall…
DLFM models complex systems with uncertainty, outperforming traditional methods.
problem Modeling highly nonlinear dynamical systems with robust uncertainty quantification.
method Deep latent force model (DLFM) using physics-informed kernels derived from ODEs.
result DLFM achieves comparable performance to non-physics-informed models on univariate tasks and captures dynamics in real-world data.
Recent advances in analysis of subband amplitude envelopes of natural sounds have resulted in convincing synthesis, showing subband amplitudes to be a crucial component of perception. Probabilistic latent variable analysis is particularly revealing, but existing approaches don't incorporate prior knowledge about the ph…
Hybrid models combine domain knowledge and data-driven learning for Earth observation.
problem Challenges in modelling Earth observation data with either purely mechanistic or data-driven methods.
method Gaussian process convolution models, specifically latent force models (LFMs), integrating physical knowledge into multioutput GP models.
result Model automatically estimates soil moisture persistence and discovers latent forces related to precipitation.
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feas…
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also show how the Gaussian process prior used in LFMs can be equivalently formulated…
The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.
problem Learning nonparametric nonlinear operators from data.
method NVKM model using Volterra series and Gaussian processes for unobserved and observed input functions.
result The NVKM model can perform both single and multiple output regression and system identification.
The paper presents a method to infer unknown forcing functions in differential equations using Gaussian processes and adjoints.
problem Inferring unknown forcing functions in differential equations from noisy observations.
method Using adjoint methods to efficiently infer Gaussian process (GP) driven differential equations, with truncated basis expansions of the GP kernel.
result Efficient Bayesian inference of forcing functions modeled as GPs using adjoints, with lower computation than MCMC methods.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
A scalable factorized Gaussian process VAE for faster inference.
problem Inference bottlenecks in Gaussian process VAEs.
method Factorizes latent kernel across auxiliary features, leveraging independence.
result Significant speed-up in inference time (in theory and practice).
TPLVM models portfolio construction for non-Gaussian financial data.
problem Optimal asset allocation in finance with non-Gaussian fluctuations.
method Student's t-process latent variable model (TPLVM) for portfolio optimization.
result TPLVM outperforms Gaussian process latent variable model in minimum-variance portfolio construction.
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to infe…
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Paper presents a reparameterized DP-DLGMM for clustering.
problem Non-parametric DP priors in DLGMM are hard to couple with variational inference.
method Closed-form updates for DP-DLGMM's variational posterior.
result Model generates realistic samples and performs competitively in semi-supervised settings.
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number of latent processes and their kernels. These choices are typically done manuall…
Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these conditions and generalize to a new one with few data? We present a new model ca…
Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approachstat.ML
A new model captures car-following and lane-changing behaviors in traffic.
problem Modeling stochastic microscopic traffic behaviors.
method Physics regularized Gaussian process (PRGP) approach.
result The proposed model outperforms previous methods in estimation precision.
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …
Extends Gaussian process regression for non-Gaussian data.
problem Inadequate modeling of uncertainty and over-smoothing in non-Gaussian datasets.
method Time-changed Gaussian processes with Lévy processes.
result Improved modeling of heavy-tailed non-Gaussian behaviors.
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.
GPIRT uses Gaussian processes to estimate latent traits and IRFs from binary responses.
problem Nonparametric IRT models struggle to estimate flexible IRFs and latent traits simultaneously.
method GPIRT employs Gaussian process priors to relax IRF assumptions while estimating latent traits.
result GPIRT provides a flexible solution to IRT challenges, including active learning.
This paper tackles federated learning for automatic latent variable selection in multi-output Gaussian processes.
problem Challenges in determining the adequate number of latent processes and relying on centralized learning for privacy and computational issues.
method Proposes a hierarchical model with spike-and-slab priors for automatic latent process selection and variational inference-based federated learning algorithm.
result Demonstrates the advantageous features of the proposed federated approach through simulations and real-world data.
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences among observe…
New model improves traffic flow predictions with physics and machine learning.
problem Inaccurate predictions in traffic flow modeling with small or noisy datasets.
method Developed a physics regularized Gaussian process (PRGP) model to encode physical models into ML architecture and regularize the training process.
result The PRGP model outperforms previous methods in estimation precision and input robustness.
New method combines ODE solvers with Bayesian inference for efficient model training.
problem Combining ODE solvers with Bayesian inference for efficient model training.
method Probabilistic state space model using extended Kalman filter for joint inference from differential equations and data.
result Efficient approximate Bayesian inference on latent force and ODE solution.
Proposes a framework to improve VAE latent codes using mutual information.
problem Lack of explicit measure for VAE latent variable quality.
method Variational Mutual Information Maximization Framework.
result Improves relationships between latent codes and observations.
Machine learning reconstructs aerodynamic forces from noisy data.
problem Accurately modeling aerodynamic forces with limited or noisy data.
method Physics-informed Gaussian processes trained on noisy structural responses.
result Strong agreement between true and predicted aerodynamic loads.
We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian distribution, which makes the model unsuited for data with e.g. categorical or nominal a…
The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …
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.