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It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…

Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

This paper considers adiabatic reduction in both discrete and continuous models of stochastic gene expression. In gene expression models, the concept of bursting is a production of several molecules simultaneously and is generally…

We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…

Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended timescales. Our methodology involves simulating proteins with molecular…

Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…

Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes,…

Feedback optimization is an increasingly popular control paradigm to optimize dynamical systems, accounting for control objectives that concern the system operation at steady-state. Existing feedback optimization techniques heavily rely on…

We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…

Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…

In neural networks with binary activations and or binary weights the training by gradient descent is complicated as the model has piecewise constant response. We consider stochastic binary networks, obtained by adding noises in front of…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Turbulent dynamical systems are characterized by nonlinear interactions and stochastic effects that generate coupled statistical quantities, such as non-zero higher-order moments, which are difficult to capture from data with accuracy. We…

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…