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One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the…

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…

We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hardcore repulsion on a finite one-dimensional…

A framework to learn a multi-modal distribution is proposed, denoted as the Conditional Quantum Generative Adversarial Network (C-qGAN). The neural network structure is strictly within a quantum circuit and, as a consequence, is shown to…

Generative models learn the distribution of data from a sample dataset and can then generate new data instances. Recent advances in deep learning has brought forth improvements in generative model architectures, and some state-of-the-art…

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

We present a method for using neural networks to model evolutionary population dynamics, and draw parallels to recent deep learning advancements in which adversarially-trained neural networks engage in coevolutionary interactions. We…

This paper presents a novel data-driven crowd simulation method that can mimic the observed traffic of pedestrians in a given environment. Given a set of observed trajectories, we use a recent form of neural networks, Generative Adversarial…

Generative adversarial networks (GANs) are a class of machine-learning models that use adversarial training to generate new samples with the same (potentially very complex) statistics as the training samples. One major form of training…

We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative…

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…

Consider first a memoryless population model described by the usual branching process with a given mean reproduction matrix on a finite space of types. Motivated by the consequences of atavism in Evolutionary Biology, we are interested in a…

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's…

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…

Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery.…

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…