Quantum speedup of Bayes' classifiers

Data classification is a fundamental problem in machine learning. We study quantum speedup of the supervised data classification algorithms (quadratic, linear and naïve Bayes classifiers) based on Bayes' theory. The main technique we use to achieve quantum speedup is block-encoding. However, to...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 53; no. 4; pp. 45301 - 45326
Main Author Shao, Changpeng
Format Journal Article
LanguageEnglish
Published IOP Publishing 31.01.2020
Subjects
Bayes' classifiers
machine learning
quantum algorithms
quantum computing
Online AccessGet full text
ISSN1751-8113
1751-8121
1751-8121
DOI10.1088/1751-8121/ab5d77

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Abstract Data classification is a fundamental problem in machine learning. We study quantum speedup of the supervised data classification algorithms (quadratic, linear and naïve Bayes classifiers) based on Bayes' theory. The main technique we use to achieve quantum speedup is block-encoding. However, to apply this technique effectively, we propose a general method to construct the block-encoding. As an application, we show that all the three classifiers achieve exponential speedup at the number of samples over their classical counterparts. As for the dimension of the space, quantum quadratic and linear classifiers achieve varying degrees of polynomial speedup, while quantum naïve Bayes' classifier achieves an exponential speedup. The only assumption we make is the qRAM to prepare quantum states of the input data.
AbstractList Data classification is a fundamental problem in machine learning. We study quantum speedup of the supervised data classification algorithms (quadratic, linear and naïve Bayes classifiers) based on Bayes' theory. The main technique we use to achieve quantum speedup is block-encoding. However, to apply this technique effectively, we propose a general method to construct the block-encoding. As an application, we show that all the three classifiers achieve exponential speedup at the number of samples over their classical counterparts. As for the dimension of the space, quantum quadratic and linear classifiers achieve varying degrees of polynomial speedup, while quantum naïve Bayes' classifier achieves an exponential speedup. The only assumption we make is the qRAM to prepare quantum states of the input data.
Author Shao, Changpeng
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  organization: University of Bristol School of Mathematics, Bristol, BS8 1UG, United Kingdom
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Snippet Data classification is a fundamental problem in machine learning. We study quantum speedup of the supervised data classification algorithms (quadratic, linear...
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SubjectTerms Bayes' classifiers
machine learning
quantum algorithms
quantum computing
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Title Quantum speedup of Bayes' classifiers
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