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Expressivity of deterministic quantum computation with one qubit

Physical Review A 2025年第2期111卷 022429-022429页

作者： Yujin Kim Daniel K. Park Department of Statistics and Data Science Yonsei University Seoul 03722 Republic of Korea Department of Applied Statistics Yonsei University Seoul 03722 Republic of Korea

Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.

关键词： Qubits

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Exposing factors influencing Korean leisure life satisfaction through machine learning techniques

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Discover Artificial Intelligence 2024年第1期4卷 1-15页

作者： Lee, Yong-Kwan Kim, Boohyun Kim, Jinheum Korea Culture & amp Tourism Institute Seoul07511 Korea Republic of Department of Data Science University of Suwon Hwaseong18323 Korea Republic of Department of Applied Statistics University of Suwon 17 Wauan-Gil Bongdam-Eup Hwaseong18323 Korea Republic of

This study examines factors influencing leisure life satisfaction (LLS) through machine learning techniques based on the data from the 2019 National Leisure Activity Survey in Korea. The results show that using machine learning techniques in identifying LLS influencing factors improves predictive power and helps detect effective leisure interventions. We also provide insights into the factors influencing LLS by standardizing activity measures based on leisure type and examining differences in resource accessibility and experiences across groups. The findings suggest that a diverse and balanced leisure repertoire is associated with greater levels of LLS, particularly in active leisure and social activities. However, the relationship between the repertoire of passive leisure activities and LLS is negative, suggesting that the optimal point for leisure activities lies found between various leisure experiences and limited resources. Leisure resource availability, such as expenditure, time, facilities, and interpersonal factors, may affect LLS, but varies by age. The results provide new insights and more accurate models of the factors influencing LLS and their complex relationships. © The Author(s) 2024.

关键词： Active learning

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Nonstationary Sparse Spectral Permanental Process 38

Nonstationary Sparse Spectral Permanental Process

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Sun, Zicheng Zhang, Yixuan Ling, Zenan Fan, Xuhui Zhou, Feng Center for Applied Statistics and School of Statistics Renmin University of China China School of Statistics and Data Science Southeast University United States School of EIC Huazhong University of Science and Technology China School of Computing Macquarie University Australia Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing China

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance. Code is publicly available at https://***/SZC20/DNSSPP. © 2024 Neural information processing systems foundation. All rights reserved.

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Bifurcation analysis of a diffusive radio-dependent model with spatial memory

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International Journal of Biomathematics 2024年第8期17卷 309-347页

作者： Qi An Xingyu Guo Xuebing Zhang College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 P.R.China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing 210044 P.R.China

This is an Open Access article published by World Scientific Publishing *** is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0(CC BY-NC-ND)License,which permits use,distribution and reproduction,provided that the original work is properly cited,the use is non-commercial and no modifications or adaptations are *** cognitive abilities of animals,such as memory,have a significant impact on their movement in *** this paper,we consider a radio-dependent model with memorybased diffusion under the conditions of Neumann *** stability of a positive equilibrium and the existence of the Turing-Hopf bifurcation induced by memory diffusion and memory delay are carried out in ***,our findings indicate that with a relatively short average memory period,the large memory diffusion can stabilize an otherwise unstable *** addition,the third-order truncated normal form for the Turing-Hopf bifurcation restricted to the central manifold is derived,which can reveal the generation of some steady-state and time-periodic solutions with spatial *** coefficients within the normal form are systematically determined through matrix operations,and these results can also be applied to other models with memory ***,leveraging the theoretical findings,we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing-Hopf bifurcation through numerical simulations.

关键词： Spatial memory normal form Turing-Hopf bifurcation spatio-temporal patterns periodic solutions

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Automatic Discovery of Controversial Legal Judgments by an Entropy-Based Measurement 35

Automatic Discovery of Controversial Legal Judgments by an E...

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35th International Conference on Software Engineering and Knowledge Engineering, SEKE 2023

作者： Zhou, Jing Leng, Shan Wang, Fang Wang, Hansheng Center for Applied Statistics School of Statistics Renmin University of China China Department of Statistics University of Wisconsin Madison United States Data Science Institute Shandong University China Guanghua School of Management Peking University China

The judgment of controversial cases has always been an important judicial issue, but it is not easy to discover them in practice. In this paper, based on 1,361,354 legal instruments data collected from China Judgments Online, we adopt a deep learning framework to classify 147 different kinds of crimes. The proposed method has three critical steps: 1) We adopt a deep learning model to predict crime categorization;2) With the trained model, each case is given a score vector which represents the probability that it belongs to each crime;3) With the probability score, we develop an entropy-based index to measure the controversy of each case. We find that the larger the entropy, the more inconsistent the result given by the model based on the first instance judgment. To verify the proposed entropy measure, we provide 1) two-sided evidence based on second instance judgments;2) comparison with some baseline models. Both confirm the practical usefulness of the entropy measure. Our results indicate that the proposed framework has an ability to discover potentially controversial cases. It should be noted that the goal of this study is not to substitute the model result for the judge’s decision, but to provide a guiding reference for the judicial practice of sentencing. © 2023 Knowledge Systems Institute Graduate School. All rights reserved.

关键词： Crime

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General Frameworks for Conditional Two-Sample Testing

arXiv

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arXiv 2024年

作者： Lee, Seongchan Cha, Suman Kim, Ilmun Department of Statistics and Data Science Yonsei University Seoul Korea Republic of Department of Statistics and Data Science Department of Applied Statistics Yonsei University Seoul Korea Republic of

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as domain adaptation and algorithmic fairness, where comparing two groups is essential while controlling for confounding variables. We begin by establishing a hardness result for conditional two-sample testing, demonstrating that no valid test can have significant power against any single alternative without proper assumptions. We then introduce two general frameworks that implicitly or explicitly target specific classes of distributions for their validity and power. Our first framework allows us to convert any conditional independence test into a conditional two-sample test in a black-box manner, while preserving the asymptotic properties of the original conditional independence test. The second framework transforms the problem into comparing marginal distributions with estimated density ratios, which allows us to leverage existing methods for marginal two-sample testing. We demonstrate this idea in a concrete manner with classification and kernel-based methods. Finally, simulation studies are conducted to illustrate the proposed frameworks in finite-sample scenarios. © 2024, CC BY.

关键词： Black-box testing

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Computational-Statistical Trade-off in Kernel Two-Sample Testing with Random Fourier Features

arXiv

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arXiv 2024年

作者： Choi, Ikjun Kim, Ilmun Department of Statistics and Data Science Yonsei University Seoul Korea Republic of Department of Statistics and Data Science Department of Applied Statistics Yonsei University Seoul Korea Republic of

Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high-dimensional data. Despite its success and widespread adoption, the primary limitation of the MMD test has been its quadratic-time complexity, which poses challenges for large-scale analysis. While various approaches have been proposed to expedite the procedure, it has been unclear whether it is possible to attain the same power guarantee as the MMD test at sub-quadratic time cost. To fill this gap, we revisit the approximated MMD test using random Fourier features, and investigate its computational-statistical trade-off. We start by revealing that the approximated MMD test is pointwise consistent in power only when the number of random features approaches infinity. We then consider the uniform power of the test and study the time-power trade-off under the minimax testing framework. Our result shows that, by carefully choosing the number of random features, it is possible to attain the same minimax separation rates as the MMD test within sub-quadratic time. We demonstrate this point under different distributional assumptions such as densities in a Sobolev ball. Our theoretical findings are corroborated by simulation studies. © 2024, CC BY.

关键词： Fourier transforms

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UNDERSTANDING GENERALIZATION IN QUANTUM MACHINE LEARNING WITH MARGINS

arXiv

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arXiv 2024年

作者： Hur, Tak Park, Daniel K. Department of Statistics and Data Science Yonsei University Seoul Korea Republic of Department of Applied Statistics Department of Statistics and Data Science Yonsei University Seoul Korea Republic of

Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings. In this work, we present a margin-based generalization bound for QML models, providing a more reliable framework for evaluating generalization. Our experimental studies on the quantum phase recognition (QPR) dataset demonstrate that margin-based metrics are strong predictors of generalization performance, outperforming traditional metrics like parameter count. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML through a classical-quantum hybrid approach when applied to classical data. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum computers

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Characterizations of Weighted Besov Spaces with Variable Exponents

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Acta Mathematica Sinica,English Series 2024年第11期40卷 2855-2878页

作者： Sheng Rong WANG Peng Fei GUO Jing Shi XU School of Mathematics and Statistics Hainan Normal UniversityHaikou571158P.R.China Center for Applied Mathematics of Guangxi Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationSchool of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin541004P.R.China

In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal *** we obtain decomposition characterizations of these spaces by atom,molecule and *** an applicatio... 详细信息

关键词： Besov space Muckenhoupt weight variable exponent Peetre’s maximal function atom molecule wavelet pseudo-differential operator

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TransFeat-TPP: An Interpretable Deep Covariate Temporal Point Processes 27

TransFeat-TPP: An Interpretable Deep Covariate Temporal Poin...

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27th European Conference on Artificial Intelligence, ECAI 2024

作者： Meng, Zizhuo Li, Boyu Fan, Xuhui Li, Zhidong Wang, Yang Chen, Fang Zhou, Feng Data Science Institute University of Technology Sydney Australia School of Computing Macquarie University Australia Center for Applied Statistics School of Statistics Renmin University of China China Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing China

ISBN: (纸本)9781643685489

The classical temporal point process (TPP) constructs an intensity function by taking the occurrence times into account. Nevertheless, occurrence time may not be the only relevant factor, other contextual data, termed covariates, may also impact the event evolution. Incorporating such covariates into the model is beneficial, while distinguishing their relevance to the event dynamics is of great practical significance. In this work, we propose a Transformer-based covariate temporal point process (TransFeat-TPP) model to improve the interpretability of deep covariate-TPPs while maintaining powerful expressiveness. TransFeat-TPP can effectively model complex relationships between events and covariates, and provide enhanced interpretability by discerning the importance of various covariates. Experimental results on synthetic and real datasets demonstrate improved prediction accuracy and consistently interpretable feature importance when compared to existing deep covariate-TPPs. Our code is available at https://***/waystogetthere/***. © 2024 The Authors.

关键词： Spatio-temporal data

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