Related papers: Efficient EM-Variational Inference for Hawkes Proc…
This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
We study the problem of estimating the intensity function of a covariate-driven point process based on observations of the points and covariates over a large window. We consider the nonparametric Bayesian approach, and show that a wide…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
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…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…
We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…
Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…
In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the number of points in each bin is counted. The distribution of…
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter…
Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…