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The irrelevant information principle for collective probabilistic reasoning

Martin Adamčík, George Wilmers (2014)

Kybernetika

Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, error , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the error inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...

The -product approach for linear ODEs: A numerical study of the scalar case

Pozza, Stefano, Van Buggenhout, Niel (2023)

Programs and Algorithms of Numerical Mathematics

Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...

The structure-from-motion reconstruction pipeline – a survey with focus on short image sequences

Klaus Häming, Gabriele Peters (2010)

Kybernetika

The problem addressed in this paper is the reconstruction of an object in the form of a realistically textured 3D model from images taken with an uncalibrated camera. We especially focus on reconstructions from short image sequences. By means of a description of an easy to use system, which is able to accomplish this in a fast and reliable way, we give a survey of all steps of the reconstruction pipeline. For the purpose of developing a coherent reconstruction system it is necessary to integrate...

The sum-product algorithm: algebraic independence and computational aspects

Francesco M. Malvestuto (2013)

Kybernetika

The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic...

The tree of shapes of an image

Coloma Ballester, Vicent Caselles, P. Monasse (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In [30], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation...

The tree of shapes of an image

Coloma Ballester, Vicent Caselles, P. Monasse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In [CITE], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation problem...

The UD RLS algorithm for training feedforward neural networks

Jarosław Bilski (2005)

International Journal of Applied Mathematics and Computer Science

A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.

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