On semi-supervised learning

CHOLAQUIDIS, A.; SUED, M.; FRAIMAN, R.

TEST

SPRINGER

Lugar: Berlin; Año: 2019 p. 1 - 24

1133-0686

Major efforts have been made, mostly in the machine learning literature, to constructgood predictors combining unlabelled and labelled data. These methods are known assemi-supervised. They deal with the problem of how to take advantage, if possible, ofa huge amount of unlabelled data to perform classification in situations where thereare few labelled data. This is not always feasible: it depends on the possibility to inferthe labels from the unlabelled data distribution. Nevertheless, several algorithms havebeen proposed recently. In this work, we present a new method that, under almostnecessary conditions, attains asymptotically the performance of the best theoreticalrule when the size of the unlabelled sample goes to infinity, even if the size of thelabelled sample remains fixed. Its performance and computational time are assessedthrough simulations and in the well- known ?Isolet? real data of phonemes, where astrong dependence on the choice of the initial training sample is shown. The mainfocus of this work is to elucidate when and why semi-supervised learning works inthe asymptotic regime described above. The set of necessary assumptions, althoughreasonable, show that semi-parametric methods only attain consistency for very well-conditioned problems.