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Italian Conference on Theoretical Computer Science

Quantum Algorithm for Ensemble Learning.

Antonio Macaluso, Stefano Lodi, Claudio Sartori

Published Jan 1, 2020• 3 citations
OpenAlex

Abstract

The idea of ensemble learning is to build a prediction model \nby combining the strengths of a collection of simpler base models. Al- \nthough they are extensively used, ensemble methods have high require- \nments in terms of memory and computational time. \nIn this work, we propose a quantum algorithm that allows reproducing \nensemble classification using bagging strategy. The algorithm generates \nmany sub-samples in superposition, in such a way that only a single exe- \ncution of a quantum classifier is required. In particular, the entanglement \nbetween a quantum register and different training sub-samples in super- \nposition allows obtaining a sum of individual results which gives rise to \nthe ensemble prediction. When considering the overall temporal cost of \nthe algorithm, the single base classifier impacts additively rather than \nmultiplicatively, as it usually happens in ensemble framework. Further- \nmore, given that the number of base models scales exponentially with \nthe number of qubits of the control register, our algorithm opens up the \npossibility of exponential speed-up for quantum ensemble.

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The idea of ensemble learning is to build a prediction model \nby combining the strengths of a collection of simpler base models. Al- \nthough they are extensively used, ensemble methods have high require- \nments in terms of memory and computational time. \nIn this work, we propose a quantum algorithm that allows reproducing \nensemble classification using bagging strategy. The algorithm generates \nmany sub-samples in superposition, in such a way that only a single exe- \ncution of a quantum classifier is required. In particular, the entanglement \nbetween a quantum register and different training sub-samples in super- \nposition allows obtaining a sum of individual results which gives rise to \nthe ensemble prediction. When considering the overall temporal cost of \nthe algorithm, the single base classifier impacts additively rather than \nmultiplicatively, as it usually happens in ensemble framework. Further- \nmore, given that the number of base models scales exponentially with \nthe number of qubits of the control register, our algorithm opens up the \npossibility of exponential speed-up for quantum ensemble.
Abstract Ensemble methods aggregate predictions from multiple models, typically demonstrating improved accuracy and reduced variance compared to individual classifiers. However, they often come with significant memory usage and computational time requirements. A novel quantum algorithm that leverages quantum superposition, entanglement, and interference to construct an ensemble of classification models using bagging as an aggregation strategy is introduced. Through the generation of numerous quantum trajectories in superposition, the authors achieve B transformations of the training set with only operations, allowing an exponential enlargement of the ensemble size while linearly increasing the depth of the corresponding circuit. Moreover, when assessing the algorithm's overall cost, the authors demonstrate that the training of a single weak classifier contributes additively to the overall time complexity, as opposed to the multiplicative impact commonly observed in classical ensemble methods. To illustrate the efficacy of the authors’ approach, experiments on reduced real‐world datasets utilising the IBM qiskit environment to demonstrate the functionality and performance of the proposed algorithm are introduced.
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain BBB transformations of the quantum state which encodes the training set in only log(B)log\left(B\right)log(B) operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential of quantum computing to enhance machine learning algorithms. An approach of quantum machine learning named quantum ensembles of quantum classifiers consists of using superposition to build an exponentially large ensemble of classifiers to be trained with an optimization-free learning algorithm. In this work, we investigate how the quantum ensemble works with the addition of an optimization method. Experiments using benchmark datasets show the improvements obtained with the addition of the optimization step.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which -- similar to Bayesian learning -- the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.