Related papers: A note on a system of parameters
Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…
The evaluation of recommender system fairness has become increasingly important, especially with recent legislation that emphasises the development of fair and responsible artificial intelligence. This has led to the emergence of various…
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
We prove a criterion that allows to construct units in product systems of correspondences with prescribed infinitesimal characterizations. This criterion summarizes proofs of known results and new applications. It also frees the hypothesis…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…
In this paper we investigate the problem of learning an unknown bounded function. We be emphasize special cases where it is possible to provide very simple (in terms of computation) estimates enjoying in addition the property of being…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…
These notes are concerned with the existence and the basic properties of the set-theoretic universes for nonstandard analysis, compiled by a beginner in the subject. It assumes a basic background in first-order logic, though the necessary…
A first order inference system, called R-calculus, is defined to develop the specifications. It is used to eliminate the laws which is not consistent with the user's requirements. The R-calculus consists of the structural rules, an axiom, a…
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…
In a stochastic noise setting the Lepskij balancing principle for choosing the regularization parameter in the regularization of inverse problems is depending on a parameter $\tau$ which in the currently known proofs is depending on the…
This paper proposes a max-test for testing (possibly infinitely) many zero parameter restrictions in an extremum estimation framework. The test statistic is formed by estimating key parameters one at a time based on many empirical loss…
This paper is part of a program to understand the parameter spaces of dynamical systems generated by meromorphic functions with finitely many singular values. We give a full description of the parameter space for a specific family based on…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
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].
This paper introduces an objective metric for evaluating a parsing scheme. It is based on Shannon's original work with letter sequences, which can be extended to part-of-speech tag sequences. It is shown that this regular language is an…