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Title: Correction of AI systems by linear discriminants: Probabilistic foundations
Authors: Grechuk, B
Gorban, A
Golubkov, A
Mirkes, E
Tyukin, I
First Published: 25-Jul-2018
Publisher: Elsevier
Citation: Information Sciences, 2018, 466, pp. 303-322
Abstract: Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the systems can create new errors and is not always possible due to the resources involved. The important challenge is to develop fast methods to correct errors without damaging existing skills. We formulated the technical requirements to the ‘ideal’ correctors. Such correctors include binary classifiers, which separate the situations with high risk of errors from the situations where the AI systems work properly. Surprisingly, for essentially high-dimensional data such methods are possible: simple linear Fisher discriminant can separate the situations with errors from correctly solved tasks even for exponentially large samples. The paper presents the probabilistic basis for fast non-destructive correction of AI systems. A series of new stochastic separation theorems is proven. These theorems provide new instruments for fast non-iterative correction of errors of legacy AI systems. The new approaches become efficient in high-dimensions, for correction of high-dimensional systems in high-dimensional world (i.e. for processing of essentially high-dimensional data by large systems). We prove that this separability property holds for a wide class of distributions including log-concave distributions and distributions with a special ‘SMeared Absolute Continuity’ (SmAC) property defined through relations between the volume and probability of sets of vanishing volume. These classes are much wider than the Gaussian distributions. The requirement of independence and identical distribution of data is significantly relaxed. The results are supported by computational analysis of empirical data sets.
DOI Link: 10.1016/j.ins.2018.07.040
ISSN: 0020-0255
Embargo on file until: 25-Jul-2019
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier 2019. After an embargo period this version of the paper will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Mathematics

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