Related papers: Intrinsic Gaussian Vector Fields on Manifolds
Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in…
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to…
Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…
This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
Manifold learning methods are useful for high dimensional data analysis. Many of the existing methods produce a low dimensional representation that attempts to describe the intrinsic geometric structure of the original data. Typically, this…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller…
Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…
Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…