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Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random…

Extreme Learning Machines (ELM) provide a fast alternative to traditional gradient-based learning in neural networks, offering rapid training and robust generalization capabilities. Its theoretical basis shows its universal approximation…

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and…

Neural Networks are currently one of the most widely deployed machine learning algorithms. In particular, Convolutional Neural Networks (CNNs), are gaining popularity and are evaluated for deployment in safety critical applications such as…

Quantum Machine Learning is an emerging sub-field in machine learning where one of the goals is to perform pattern recognition tasks by encoding data into quantum states. This extension from classical to quantum domain has been made…

Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of…

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as…

The Extreme Learning Machine (ELM) is a growing statistical technique widely applied to regression problems. In essence, ELMs are single-layer neural networks where the hidden layer weights are randomly sampled from a specific distribution,…

Extreme learning machine (ELM) as an emerging branch of shallow networks has shown its excellent generalization and fast learning speed. However, for blended data, the robustness of ELM is weak because its weights and biases of hidden nodes…

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…

In recent years, with the development of quantum machine learning, quantum neural networks (QNNs) have gained increasing attention in the field of natural language processing (NLP) and have achieved a series of promising results. However,…

Machine learning (ML) methods such as artificial neural networks are rapidly becoming ubiquitous in modern science, technology and industry. Despite their accuracy and sophistication, neural networks can be easily fooled by carefully…

Quantum computers progress toward outperforming classical supercomputers, but quantum errors remain their primary obstacle. The key to overcoming errors on near-term devices has emerged through the field of quantum error mitigation,…

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Feature noise and label noise are ubiquitous in practical scenarios, which pose great challenges for training a robust machine learning model. Most previous approaches usually deal with only a single problem of either feature noise or label…

Quantum Machine Learning (QML) represents a promising frontier at the intersection of quantum computing and artificial intelligence, aiming to leverage quantum computational advantages to enhance data-driven tasks. This review explores the…