Related papers: Cox processes driven by transformed Gaussian proce…
This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
The log Gaussian Cox process is a flexible class of Cox processes, whose intensity surface is stochastic, for incorporating complex spatial and time structure of point patterns. The straightforward inference based on Markov chain Monte…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
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…
The log-Gaussian Cox process (LGCP) is a popular point process for modeling non-interacting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the…
The modeling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
In the framework of the supervised learning of a real function defined on a space X , the so called Kriging method stands on a real Gaussian field defined on X. The Euclidean case is well known and has been widely studied. In this paper, we…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
This paper establishes a remarkable result regarding Palmdistributions for a log Gaussian Cox process: the reduced Palmdistribution for a log Gaussian Cox process is itself a log Gaussian Coxprocess which only differs from the original log…
Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…