Related papers: From Random Processes to Generalized Fields: A Uni…
Random fields have remained a topic of great interest over past decades for the purpose of structured inference, especially for problems such as image segmentation. The local nodal interactions commonly used in such models often suffer the…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle…
Fields offer a versatile approach for describing complex systems composed of interacting and dynamic components. In particular, some of these dynamical and stochastic systems may exhibit goal-directed behaviors aimed at achieving specific…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
A stochastic process that arises by composing a function with a Markov process is called an aggregated Markov process (AMP). The purpose of composing a Markov process with a function can be a reduction of dimensions, e.g., a projection onto…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an…
Hadwiger integrals employ the intrinsic volumes as measures for integration of real-valued functions. We provide a formula for the expected values of Hadwiger integrals of Gaussian-related random fields. The expected Hadwiger integrals of…
We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral…
We introduce a class of self-similar Gaussian processes and provide sufficient and necessary conditions for a member of the class to admit a unique small scale limit in the Skorokhod space. The class includes several well known processes.…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
The commonly accepted definition of paths starts from a random field but ignores the problem of setting joint distributions of infinitely many random variables for defining paths properly afterwards. This paper provides a turnaround that…
The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making…
Bayesian optimization is a powerful tool for expensive stochastic black-box optimization problems such as simulation-based optimization or machine learning hyperparameter tuning. Many stochastic objective functions implicitly require a…