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Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…
Learning stochastic functions from partially observed context-target pairs requires models that are expressive, uncertainty-aware, and strongly conditioned on inputs. Neural Diffusion Processes (NDPs) improve expressivity with denoising…
The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…
We propose a direct numerical method to calculate the statistics of the number of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary…
In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…
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…
Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…
The purpose of this paper is to introduce the construction of a stochastic process called ``diffusion house-moving'' and to explore its properties. We study the weak convergence of diffusion bridges conditioned to stay between two curves,…
Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…