Norm--Free Radon--Nikodym Approach to Machine Learning

Norm-Free Radon-Nikodym Approach to Machine Learning

For Machine Learning (ML) classification problem, where a vector of x–observations (values of attributes) is mapped to a single y value (class label), a generalized Radon– Nikodym type of solution is proposed. Quantum–mechanics –like probability states ψ2(x) are considered and “Cluster Centers”, corresponding to the extremums of < yψ2(x) > / < ψ2(x) >, are found from generalized eigenvalues pro...

Multiple-Instance Learning: Radon-Nikodym Approach to Distribution Regression Problem

For distribution regression problem, where a bag of x–observations is mapped to a single y value, a one–step solution is proposed. The problem of random distribution to random value is transformed to random vector to random value by taking distribution moments of x observations in a bag as random vector. Then Radon–Nikodym or least squares theory can be applied, what give y(x) estimator. The pr...

A Radon-Nikodym approach to measure information

Reasonable non–Radon–Nikodym idealss

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

Dilatation structures with the Radon-Nikodym property

The notion of a dilatation structure stemmed out from my efforts to understand basic results in sub-Riemannian geometry, especially the last section of the paper by Belläıche [2] and the intrinsic point of view of Gromov [5]. In these papers, as in other articles devoted to sub-Riemannian geometry, fundamental results admiting an intrinsic formulation were proved using differential geometry too...