Related papers: Stochastic Nondeterminism and Effectivity Function…
In decentralized stochastic control (or stochastic team theory) and game theory, if there is a pre-defined order in a system in which agents act, the system is called \textit{sequential}, otherwise it is non-sequential. Much of the…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As…
In this work we study the self-integral of a function-measure kernel and its importance on stochastic integration. A continuous-function measure kernel $K$ over $D \subset \mathbb{R}^{d}$ is a function of two variables which acts as a…
The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying…
This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…
Effectivity functions are the basic formalism for investigating the semantics game logic. We discuss algebraic properties of stochastic effectivity functions, in particular the relationship to stochastic relations, morphisms and congruences…
We define decision-making functions which arise from studying the multidimensional generalization of the weighted Bajraktarevi\'c means. It allows a nonlinear approach to optimization problems. These functions admit several interesting…
Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…