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This paper describes how to make the problem of binary classification amenable to quantum computing. A formulation is employed in which the binary classifier is constructed as a thresholded linear superposition of a set of weak classifiers.…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer…
Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware…
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…
Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the…
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…
We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
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…
Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes.…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
In this work, we introduce a novel Quadratic Binary Optimization (QBO) framework for training a quantized neural network. The framework enables the use of arbitrary activation and loss functions through spline interpolation, while Forward…
We investigate the performance of penalty-based quantum annealing (PQA) and constrained quantum annealing (CQA) in solving the graph partitioning problem under various noise models, including depolarizing, bit-flip, and phase-flip noise. We…
Object grasping is a crucial technology enabling robots to perceive and interact with the environment sufficiently. However, in practical applications, researchers are faced with missing or noisy ground truth while training the…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
We prove that the empirical risk of most well-known loss functions factors into a linear term aggregating all labels with a term that is label free, and can further be expressed by sums of the loss. This holds true even for non-smooth,…
Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is…
Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…
People learn to discriminate between classes without explicit exposure to negative examples. On the contrary, traditional machine learning algorithms often rely on negative examples, otherwise the model would be prone to collapse and…