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Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…

Neural network-based algorithms have garnered considerable attention in condensed matter physics for their ability to learn complex patterns from very high dimensional data sets towards classifying complex long-range patterns of…

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based…

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult…

Deep Neural Networks (DNNs) typically require massive amount of computation resource in inference tasks for computer vision applications. Quantization can significantly reduce DNN computation and storage by decreasing the bitwidth of…

We propose an online inference method for censored quantile regression with streaming data sets. A key strategy is to approximate the martingale-based unsmooth objective function with a quadratic loss function involving a well-justified…

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce…

Combining the advantages of quantum computing and neural networks, quantum neural networks (QNNs) have gained considerable attention recently. However, because of the lack of quantum resource, it is costly to train QNNs. In this work, we…

Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading…

Quantum Neural Networks (QNNs) represent a promising direction within Quantum Machine Learning (QML), yet their realization on noisy intermediate-scale quantum (NISQ) devices remains constrained by decoherence, gate imperfections,…

This paper addresses the challenge of integrating sequentially arriving data within the quantile regression framework, where the number of features is allowed to grow with the number of observations, the horizon is unknown, and memory is…

The composite quantile regression (CQR) was introduced by Zou and Yuan [Ann. Statist. 36 (2008) 1108--1126] as a robust regression method for linear models with heavy-tailed errors while achieving high efficiency. Its penalized counterpart…

Convolutional neural networks are capable of learning powerful representational spaces, which are necessary for tackling complex learning tasks. However, due to the model capacity required to capture such representations, they are often…

A significant challenge in the field of quantum machine learning (QML) is to establish applications of quantum computation to accelerate common tasks in machine learning such as those for neural networks. Ridgelet transform has been a…

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…

Quantum Convolutional Neural Networks (QCNNs) are widely regarded as a promising model for Quantum Machine Learning (QML). In this work we tie their heuristic success to two facts. First, that when randomly initialized, they can only…

Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. This result leads to a general belief that a deep QNN will not be…

Quantification of Uncertainty in predictions is a challenging problem. In the classification settings, although deep learning based models generalize well, class probabilities often lack reliability. Calibration errors are used to quantify…

Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the…