Abstract Learning from only positive and unlabeled (PU) data has broad applications in fields such as web data mining, product recommendations and medical diagnosis, which aims to train a binary classifier in the absence of negative labeled data. However, due to the lack of negative label information, prevailing PU learning methods usually rely on prior knowledge of unknown class distributions heavily. In fact, without additional constraints imposed by the prior knowledge, a direct learning strategy to coordinate the underlying clustering information in unlabeled data with the label information from positive training data is often considered challenging. To tackle this challenge, we propose a direct PU learning strategy using quantum formalization. By employing neural networks as backends, the samples are mapped into two-qubit composite systems, which should be understood here as mathematical entities encapsulating various classical distributions of two classical bits. Subsequently, the two qubits within the systems are trained to be as independent as possible from each other, capturing patterns of different classes. At the same time, their measurement results serving as the model outputs are encouraged to be maximally dissimilar. These characteristics enable effective training of classifiers on PU data. After formulating an appropriate discriminant rule, we introduce a quantum-inspired PU method named qPU using the direct learning strategy. This method not only has the potential to alleviate parameter sensitivity issues caused by prior estimation in other methods but is also straightforward to implement. Finally, experiments conducted on 13 classical datasets validate the effectiveness of qPU.
Abstract Learning from only positive and unlabeled (PU) data has broad applications in fields such as web data mining, product recommendations and medical diagnosis, which aims to train a binary classifier in the absence of negative labeled data. However, due to the lack of negative label information, prevailing PU learning methods usually rely on prior knowledge of unknown class distributions heavily. In fact, without additional constraints imposed by the prior knowledge, a direct learning strategy to coordinate the underlying clustering information in unlabeled data with the label information from positive training data is often considered challenging. To tackle this challenge, we propose a direct PU learning strategy using quantum formalization. By employing neural networks as backends, the samples are mapped into two-qubit composite systems, which should be understood here as mathematical entities encapsulating various classical distributions of two classical bits. Subsequently, the two qubits within the systems are trained to be as independent as possible from each other, capturing patterns of different classes. At the same time, their measurement results serving as the model outputs are encouraged to be maximally dissimilar. These characteristics enable effective training of classifiers on PU data. After formulating an appropriate discriminant rule, we introduce a quantum-inspired PU method named qPU using the direct learning strategy. This method not only has the potential to alleviate parameter sensitivity issues caused by prior estimation in other methods but is also straightforward to implement. Finally, experiments conducted on 13 classical datasets validate the effectiveness of qPU.
Positive unlabeled (PU) learning is a semi-supervised machine learning (ML) approach to a binary classification problem where a small subset of the data has positive labels, and the rest of the data is unlabeled. PU learning algorithms can be very efficient at reducing the computational cost of training ML classifiers because the labeling of data for supervised machine learning algorithms is time intensive. In this study, we develop new quantum PU (QPU) learning methods for photovoltaic (PV) fault detection and perform comparative analysis with classical PU learning methods. Quantum circuits for PU learning are designed and evaluated in this study. In addition, we examine various quantum machine learning (QML) and PU learning challenges including quantum measurement noise. As with many QML simulations, the presence of quantum noise and the heavy computational and memory requirements affect classification accuracy. Nevertheless, regardless of quantum noise effects and limited computational resources, our initial designs of quantum PU learning circuits achieved an accuracy score of 79.6%. This was achieved by implementing QPU learning with a quantum-classical hybrid neural network (QNN) architecture. In our study, we present simulation results with and without quantum noise models for comparison purposes.
Abstract Entanglement detection, the process of verifying quantum entanglement is a fundamental challenge in quantum information processing. Various approaches have been proposed to address this challenge, with many recent studies applying supervised machine learning methods. While these methods have demonstrated high accuracy in entanglement detection, it is reasonable to assume that the entangled states themselves are not definitively known. To address this limitation, we have devised a machine learning method for entanglement detection based on positive-unlabeled learning, a classical machine learning framework that does not use label information from negative data. Using a deep neural network model to synthetic dataset under the assumption of mixed states, we conducted experiments on a classical computer to valid the effectiveness and characteristics of the proposed method. Our approach introduces a novel framework that accounts for the data generation constraints in the training process of entanglement detector, thereby advancing machine learning techniques in quantum information science.
Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial labeled training set for supervised learning. Human annotators, often experts, provide labels for samples through additional experiments, adding to the training cost. To mitigate this expense, there is a quest for methods that maintain model performance over fully labeled datasets while requiring fewer labeled samples in practice, thereby extending few-shot learning to the quantum realm. Quantum active learning estimates the uncertainty of quantum data to select the most informative samples from a pool for labeling. Consequently, a QML model is supposed to accumulate maximal knowledge as the training set comprises labeled samples selected via sampling strategies. Notably, the QML models trained within the QAL framework are not restricted to specific types, enabling performance enhancement from the model architecture's perspective towards few-shot learning. Recognizing symmetry as a fundamental concept in physics ubiquitous across various domains, we leverage the symmetry inherent in quantum states induced by the embedding of classical data for model design. We employ an equivariant QNN capable of generalizing from fewer data with geometric priors. We benchmark the performance of QAL on two classification problems, observing both positive and negative results. QAL effectively trains the model, achieving performance comparable to that on fully labeled datasets by labeling less than 7\% of the samples in the pool with unbiased sampling behavior. Furthermore, we elucidate the negative result of QAL being overtaken by random sampling baseline through miscellaneous numerical experiments. (character count limit, see the main text)
This paper introduces an innovative theoretical framework for quantum-inspired data embeddings, grounded in foundational concepts of quantum mechanics such as superposition and entanglement. This approach aims to advance semi-supervised learning in contexts characterized by limited labeled data by enabling more intricate and expressive embeddings that capture the underlying structure of the data effectively. Grounded in foundational quantum mechanics concepts such as superposition and entanglement, this approach redefines data representation by enabling more intricate and expressive embeddings. Emulating quantum superposition encodes each data point as a probabilistic amalgamation of multiple feature states, facilitating a richer, multidimensional representation of underlying structures and patterns. Additionally, quantum-inspired entanglement mechanisms are harnessed to model intricate dependencies between labeled and unlabeled data, promoting enhanced knowledge transfer and structural inference within the learning paradigm. In contrast to conventional quantum machine learning methodologies that often rely on quantum hardware, this framework is fully realizable within classical computational architectures, thus bypassing the practical limitations of quantum hardware. The versatility of this model is illustrated through its application to critical domains such as medical diagnosis, resource-constrained natural language processing, and financial forecasting—areas where data scarcity impedes the efficacy of traditional models. Experimental evaluations reveal that quantum-inspired embeddings substantially outperform standard approaches, enhancing model resilience and generalization in high-dimensional, low-sample scenarios. This research marks a significant stride in integrating quantum theoretical principles with classical machine learning, broadening the scope of data representation and semi-supervised learning while circumventing the technological barriers of quantum computing infrastructure.
Abstract Classification can be performed using either a discriminative or a generative learning approach. Discriminative learning consists of constructing the conditional probability of the outputs given the inputs, while generative learning consists of constructing the joint probability density of the inputs and outputs. Although most classical and quantum methods are discriminative, there are some advantages of the generative learning approach. For instance, it can be applied to unsupervised learning, statistical inference, uncertainty estimation, and synthetic data generation. In this article, we present a quantum generative multiclass classification strategy, called quantum generative classification (QGC). This model uses a variational quantum algorithm to estimate the joint probability density function of features and labels of a data set by means of a mixed quantum state. We also introduce a quantum map called quantum-enhanced Fourier features, which leverages quantum superposition to prepare high-dimensional data samples in quantum hardware using a small number of qubits. We show that the QGC algorithm can be viewed as a Gaussian mixture that reproduces a kernel Hilbert space of the training data. In addition, we developed a hybrid quantum–classical neural network that shows that it is possible to perform generative classification on high-dimensional data sets. The method was tested on various low- and high-dimensional data sets including the 10-class MNIST and Fashion-MNIST data sets, illustrating that the generative classification strategy is competitive against other previous quantum models.
Pattern recognition is a central topic in learning theory, with numerous applications such as voice and text recognition, image analysis and computer diagnosis. The statistical setup in classification is the following: we are given an i.i.d. training set ( X 1 , Y 1 ), ... , ( X n , Y n ), where X i represents a feature and Y i ∊{0, 1} is a label attached to that feature. The underlying joint distribution of ( X , Y ) is unknown, but we can learn about it from the training set, and we aim at devising low error classifiers f: X → Y used to predict the label of new incoming features. In this paper, we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown mixed qubit states. Given a number of 'training' copies from each of the states, we would like to 'learn' about them by performing a measurement on the training set. The outcome is then used to design measurements for the classification of future systems with unknown labels. We found the asymptotically optimal classification strategy and show that typically it performs strictly better than a plug-in strategy, which consists of estimating the states separately and then discriminating between them using the Helstrom measurement. The figure of merit is given by the excess risk equal to the difference between the probability of error and the probability of error of the optimal measurement for known states. We show that the excess risk scales as n −1 and compute the exact constant of the rate.