On The Radon–Nikodym Machine Learning Parallelization

Abstract

A novel Radon–Nikodym approach to machine learning (ML) is developed, implemented numerically, tested on various datasets, and it’s parallelization is discussed. It consists in building a “wavefunction” ψ(x), a linear function on input attributes x then constructing a classificator of the form ⟨ψ2f⟩/⟨ψ2⟩. The solution is obtained from a generalized eigenproblem |f|ψ[i]⟩ = λ[i]|ψ[i]⟩ with left– and right– hand side matrices calculated from the input dataset. A solution to classification problem (predict f on an unseen x) is found without using a norm testing how predicted f differs from the one observed. Possible outcomes and their probabilities are obtained separately using the Lebesgue quadrature technique, this makes the method robust to input data with outliers, spikes, etc. A remarkable feature is the knowledge of the invariant group (what input attributes transforms do not change the solution). Radon–Nikodym approach is typically slower than the other methods used, this is the cost of being a “norm–free”. A parallel implementation is expected to improve this deficiency.