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This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

Representations of measures of concordance in terms of Pearson' s correlation coefficient are studied. All transforms of random variables are characterized such that the correlation coefficient of the transformed random variables is a…

Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…

In the context of nucleon structure, the Wigner distribution has been commonly used to visualize the phase-space distribution of quarks and gluons inside the nucleon. However, the Wigner distribution does not allow for a probabilistic…

We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural…

The de-excitation of compound nuclei has been successfully described for several decades by means of statistical models. However, accurate predictions require some fine-tuning of the model parameters. This task can be simplified by studying…

Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…

Out-of-distribution data and anomalous inputs are vulnerabilities of machine learning systems today, often causing systems to make incorrect predictions. The diverse range of data on which these models are used makes detecting atypical…

Deep neural networks (DNN) have been deployed in many software systems to assist in various classification tasks. In company with the fantastic effectiveness in classification, DNNs could also exhibit incorrect behaviors and result in…

In this paper, I design a new statistical abstract model for studying quantum error propagation. For each circuit, I give the algorithm to construct the Error propagation space-time graph(\textbf{EPSTG}) graph as well as the bipartite…

We provide a new approach to error mitigation for quantum chemistry simulation that uses a Bravyi-Kitaev Superfast encoding to implement a quantum error detecting code within the fermionic encoding. Our construction has low-weight parity…

Reconstruction error is a prevalent score used to identify anomalous samples when data are modeled by generative models, such as (variational) auto-encoders or generative adversarial networks. This score relies on the assumption that normal…

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Models notoriously suffer from dataset biases which are detrimental to robustness and generalization. The identify-emphasize paradigm shows a promising effect in dealing with unknown biases. However, we find that it is still plagued by two…

As machine learning becomes increasingly central to molecular design, it is vital to ensure the reliability of learnable protein-ligand scoring functions on novel protein targets. While many scoring functions perform well on standard…

Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal inference provides a pivotal and flexible instrument for assessing the uncertainty of…

The use of deep learning for medical imaging has seen tremendous growth in the research community. One reason for the slow uptake of these systems in the clinical setting is that they are complex, opaque and tend to fail silently. Outside…

Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…

In industrial settings, surface defects on steel can significantly compromise its service life and elevate potential safety risks. Traditional defect detection methods predominantly rely on manual inspection, which suffers from low…