Related papers: Revisiting Continuous-Time Trajectory Estimation v…

A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of…

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…

Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…

In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized…

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent…

We present a continuous time state estimation framework that unifies traditionally individual tasks of smoothing, tracking, and forecasting (STF), for a class of targets subject to smooth motion processes, e.g., the target moves with nearly…

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…

Gaussian processes (GPs) are becoming a standard tool to build terrain representations thanks to their capacity to model map uncertainty. This effectively yields a reliability measure of the areas of the map, which can be directly utilized…

In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC)…

This paper proposes a parallel-in-time method for computing continuous-time maximum-a-posteriori (MAP) trajectory estimates of the states of partially observed stochastic differential equations (SDEs), with the goal of improving…

Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and…

Graph dynamical systems (GDS) model dynamic processes on a (static) graph. Stochastic GDS has been used for network-based epidemics models such as the contact process and the reversible contact process. In this paper, we consider stochastic…

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

Accurate, efficient, and robust state estimation is more important than ever in robotics as the variety of platforms and complexity of tasks continue to grow. Historically, discrete-time filters and smoothers have been the dominant…

Survivors of childhood cancer need lifelong monitoring for side effects from radiotherapy. However, longitudinal data from routine monitoring is often infrequently and irregularly sampled, and subject to inaccuracies. Due to this,…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant…

We propose Video Gaussian Masked Autoencoders (Video-GMAE), a self-supervised approach for representation learning that encodes a sequence of images into a set of Gaussian splats moving over time. Representing a video as a set of Gaussians…