Related papers: Identification of Gaussian Process State Space Mod…

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…

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

Inferring the posterior distribution in SLAM is critical for evaluating the uncertainty in localization and mapping, as well as supporting subsequent planning tasks aiming to reduce uncertainty for safe navigation. However, real-time full…

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors.…

We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs),…

Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…

This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at…

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high…

We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…