Related papers: The Marcinkiewicz-type discretization theorems
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{\'e}r-Lundberg…
Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…
Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line…
Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…
Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and…
An empirical investigation of the interaction of sample size and discretization - in this case the entropy-based method CAIM (Class-Attribute Interdependence Maximization) - was undertaken to evaluate the impact and potential bias…
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].
The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…