Related papers: Modified Galton-Watson processes with immigration …

In the description of the production properties of gauge bosons (W+/W-, Z0, gamma) at colliders, the lowest-order graph normally is not sufficient. The contributions of higher orders can be introduced either by an explicit order-by-order…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Generative adversarial networks (GANs) have emerged as a powerful tool for generating high-fidelity data. However, the main bottleneck of existing approaches is the lack of supervision on the generator training, which often results in…

A control strategy for the electrical current in GMAW processes is proposed. The control is in closed-loop, designed by formal methods, based on a mathematical model of the electrical behavior of the GMAW process, and implemented in C+…

We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying Galton-Watson process to describe the evolution of…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work,…

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

The simple Galton--Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Mat\'ern covariance function,…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…

Multivariate time-series data are used in many classification and regression predictive tasks, and recurrent models have been widely used for such tasks. Most common recurrent models assume that time-series data elements are of equal length…

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…

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only…

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…

The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equations, or the design of curves and surfaces. Numerous methods…

Branching processes model the evolution of populations of agents that randomly generate offsprings. These processes, more patently Galton-Watson processes, are widely used to model biological, social, cognitive, and technological phenomena,…

Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…