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Annals of Computer Science and Information Systems

A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

Venelin Todorov, Stoyan Apostolov, Ivan Dimov, Stefka Stoyanova Fidanova

Published Sep 26, 2020• 0 citations
Publisher

Abstract

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning.A fundamental problem in this area is the accurate evaluation of multidimensional integrals.An introduction to the theory of the stochastic optimal generating vectors has been given.A new optimized lattice sequence with a special choice of the optimal generating vector has been applied to compute multidimensional integrals up to 30-dimensions.Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.

DOI
10.15439/2020f110

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Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.
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Multidimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging problems of multidimensional optimization, it was suggested to use the randomized algorithms of stochastic approximation with perturbed input which have simple forms and provide consistent estimates of the unknown parameters for observations under “almost arbitrary” noise. They are easily “incorporated” in the design of quantum devices to estimate gradient vector of a multi-variable function.