Related papers: A structural equation formulation for general quas…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…
This paper establishes the mean-square convergence of a new stochastic, parameterized leapfrog scheme introduced in our companion paper Mazumder et al. (2026) for Hamiltonian systems with Gaussian process potentials. We consider a one-step…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
In this study, we propose a family of correlation structures for crossover designs with repeated measures for both, Gaussian and non-Gaussian responses using generalized estimating equations (GEE). The structure considers two matrices: one…
This paper focuses on developing a framework for constructing quasi-interpolation with the highest achievable approximation order from generalized Gaussian kernels with the help of kernel restriction trick and periodization technique. We…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
The integration of renewable energy sources (RES) into power grids presents significant challenges due to their intrinsic stochasticity and uncertainty, necessitating the development of new techniques for reliable and efficient forecasting.…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Seismic fragility curves have been introduced as key components of Seismic Probabilistic Risk Assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
We present a new, elementary way to obtain axially symmetric Gaussian processes on the sphere, in order to accommodate for the directional anisotropy of global climate data in geostatistical analysis.
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…