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arXiv:2102.00949

Quantum Inspired Adaptive Boosting

Bálint Daróczy, Katalin Friedl, László Kabódi, Attila Pereszlényi, Daniel Attila Szabo

Published Feb 1, 2021• 0 citations
arXivHTMLPDF

Abstract

Building on the quantum ensemble based classifier algorithm of Schuld and Petruccione [arXiv:1704.02146v1], we devise equivalent classical algorithms which show that this quantum ensemble method does not have advantage over classical algorithms. Essentially, we simplify their algorithm until it is intuitive to come up with an equivalent classical version. One of the classical algorithms is extremely simple and runs in constant time for each input to be classified. We further develop the idea and, as the main contribution of the paper, we propose methods inspired by combining the quantum ensemble method with adaptive boosting. The algorithms were tested and found to be comparable to the AdaBoost algorithm on publicly available data sets.

DOI
10.48550/arxiv.2102.00949

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Building on the quantum ensemble based classifier algorithm of Schuld and Petruccione [arXiv:1704.02146v1], we devise equivalent classical algorithms which show that this quantum ensemble method does not have advantage over classical algorithms. Essentially, we simplify their algorithm until it is intuitive to come up with an equivalent classical version. One of the classical algorithms is extremely simple and runs in constant time for each input to be classified. We further develop the idea and, as the main contribution of the paper, we propose methods inspired by combining the quantum ensemble method with adaptive boosting. The algorithms were tested and found to be comparable to the AdaBoost algorithm on publicly available data sets.
In this work, we consider the performance of using a quantum algorithm to predict the result of a binary classification problem when a machine learning model is an ensemble of any simple classifiers. This approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let N be the number of classifiers from an ensemble model and O(T) be the running time of prediction of one classifier. In classical case, the final result is obtained by ”averaging” outcomes of all ensemble model’s classifiers. The running time in classical case is O (N · T). We propose an algorithm that works in O (√N · T ).
In the noisy intermediate-scale quantum (NISQ) era, the capabilities of variational quantum algorithms are greatly constrained due to a limited number of qubits and the shallow depth of quantum circuits. We may view these variational quantum algorithms as weak learners in supervised learning. Ensemble methods are general approaches to combining weak learners to construct a strong one in machine learning. In this paper, by focusing on classification, we theoretically establish and numerically verify a learning guarantee for quantum adaptive boosting (AdaBoost). The supervised-learning risk bound describes how the prediction error of quantum AdaBoost on binary classification decreases as the number of boosting rounds and sample size increase. We further empirically demonstrate the advantages of quantum AdaBoost by focusing on a 4-class classification. The quantum AdaBoost not only outperforms several other ensemble methods, but in the presence of noise it can also surpass the ideally noiseless but unboosted primitive classifier after only a few boosting rounds. Our work indicates that in the current NISQ era, introducing appropriate ensemble methods is particularly valuable in improving the performance of quantum machine learning algorithms.
Abstract Boosting is an ensemble learning method that converts a weak learner into a strong learner in the PAC learning framework. The AdaBoost algorithm is a well-known classical boosting algorithm for weak learners with binary hypotheses. Recently, Arunachalam and Maity presented the first quantum boosting algorithm by quantizing AdaBoost. Their algorithm, which we refer to as QAdaBoost hereafter, is a quantum adaptation of AdaBoost and only works for the binary hypothesis case. QAdaBoost is quadratically faster than AdaBoost in terms of the VC dimension of the hypothesis class of the weak learner. However, QAdaBoost is polynomially worse in the bias of the weak learner. In this work, we address an open question by Izdebski et al. on the existence of boosting algorithms for quantum weak learners with non-binary hypotheses. We answer this question in the affirmative by developing the QRealBoost algorithm motivated by the classical RealBoost algorithm. The main technical challenge was to provide provable guarantees for convergence, generalization bounds, and quantum speedup, given that quantum subroutines are noisy and probabilistic. We prove that QRealBoost retains the quadratic speedup of QAdaBoost over AdaBoost and further achieves a polynomial speedup over QAdaBoost in terms of both the bias of the learner and the time taken by the learner to learn the target concept class. Finally, we perform empirical evaluations on QRealBoost and report encouraging observations on quantum simulators by benchmarking the convergence performance of QRealBoost against QAdaBoost, AdaBoost, and RealBoost on a subset of the MNIST dataset and Breast Cancer Wisconsin dataset.
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.
The principle and theory of quantum computation are investigated by researchers for many years, and further applied to improve the efficiency of classical machine learning algorithms. Based on physical mechanism, a quantum version of AdaBoost (Adaptive Boosting) training algorithm is proposed in this paper, of which purpose is to construct a strong classifier. In the proposed scheme with cluster state in quantum mechanism is to realize the weak learning algorithm, and then update the corresponding weight of examples. As a result, a final classifier can be obtained by combining efficiently weak hypothesis based on measuring cluster state to reweight the distribution of examples.