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We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…
Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…
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…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…
We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method, or form of NEUS. We prove convergence of the method under…
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
We prove that time dynamics of a stochastic process of pure coagulation is given by a time dependent Gibbs distribution if and only if rates of single coagulations have the form $\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrary nonnegative…
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…
We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…