Norm-Free Radon-Nikodym Approach to Machine Learning

نویسنده

Vladislav Gennadievich Malyshkin

چکیده

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 problem. The eigenvalues give possible y[i] outcomes and corresponding to them eigenvectors ψ[i](x) define “Cluster Centers”. The projection of a ψ state, localized at given x to classify, on these eigenvectors define the probability of y[i] outcome, thus avoiding using a norm (L2 or other types), required for “quality criteria” in a typical Machine Learning technique. A coverage of each ‘Cluster Center” is calculated, what potentially allows to separate system properties (described by y[i] outcomes) and system testing conditions (described by C [i] coverage). As an example of such application y distribution estimator is proposed in a form of pairs (y[i], C [i]), that can be considered as Gauss quadratures generalization. This estimator allows to perform y probability distribution estimation in a strongly non–Gaussian case.

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