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The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Re-ranking the data sequence after each new observation can become too intensive computationally.…

Statistics Theory · Mathematics 2018-12-27 W. J. Conover , Victor G. Tercero , Alvaro E. Cordero-Franco

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…

Quantum Physics · Physics 2018-01-01 Jacob Miller , Stephen Sanders , Akimasa Miyake

In many model-based diagnosis applications it is impossible to provide such a set of observations and/or measurements that allow to identify the real cause of a fault. Therefore, diagnosis systems often return many possible candidates,…

Artificial Intelligence · Computer Science 2016-12-19 Patrick Rodler , Wolfgang Schmid , Kostyantyn Shchekotykhin

In this paper, we propose a practically efficient model for securely computing rank-based statistics, e.g., median, percentiles and quartiles, over distributed datasets in the malicious setting without leaking individual data privacy. Based…

Cryptography and Security · Computer Science 2023-02-17 Nan Wang , Sid Chi-Kin Chau

This paper outlines a unified framework for high dimensional variable selection for classification problems. Traditional approaches to finding interesting variables mostly utilize only partial information through moments (like mean…

Methodology · Statistics 2016-11-25 S. Mukhopadhyay , Emanuel Parzen , S. N. Lahiri

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…

Machine Learning · Statistics 2022-03-01 Ian Osband , Zheng Wen , Seyed Mohammad Asghari , Vikranth Dwaracherla , Xiuyuan Lu , Benjamin Van Roy

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…

Machine Learning · Statistics 2015-06-16 Kacper Chwialkowski , Aaditya Ramdas , Dino Sejdinovic , Arthur Gretton

Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…

Quantum Physics · Physics 2022-01-11 Yu. I. Bogdanov , B. I. Bantysh , N. A. Bogdanova , K. B. Koksharov , V. F. Lukichev

Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular…

Quantum Physics · Physics 2009-11-11 W. J. Munro , Kae Nemoto , T. P. Spiller , S. D. Barrett , Pieter Kok , R. G. Beausoleil

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…

Statistics Theory · Mathematics 2007-06-13 Richard D. Gill

We study linear quantile regression models when regressors and/or dependent variable are not directly observed but estimated in an initial first step and used in the second step quantile regression for estimating the quantile parameters.…

Econometrics · Economics 2020-12-29 Jayeeta Bhattacharya

For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…

Methodology · Statistics 2015-08-04 Steven P. Ellis , Arno Klein

The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…

Quantum Physics · Physics 2023-04-20 Sergey V. Ulyanov , Viktor S. Ulyanov

Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity…

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…

Quantum Physics · Physics 2022-03-09 Dorit Aharonov , Jordan Cotler , Xiao-Liang Qi

The statistical problem of using an initial sample to estimate the number of species in a larger sample has found important applications in fields far removed from ecology. Here we address the general problem of estimating the number of…

Methodology · Statistics 2018-05-16 Chao Deng , Timothy Daley , Peter Calabrese , Jie Ren , Andrew D. Smith

Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…

Computational Geometry · Computer Science 2023-07-19 Suraj Shetiya , Shohedul Hasan , Abolfazl Asudeh , Gautam Das

Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…

Quantum Physics · Physics 2023-02-10 Tobias Haug , Chris N. Self , M. S. Kim

The r largest order statistics approach is widely used in extreme value analysis because it may use more information from the data than just the block maxima. In practice, the choice of r is critical. If r is too large, bias can occur; if…

Methodology · Statistics 2018-06-13 Brian Bader , Jun Yan , Xuebin Zhang

We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…

Quantum Physics · Physics 2024-05-22 Jiachen Hu , Tongyang Li , Xinzhao Wang , Yecheng Xue , Chenyi Zhang , Han Zhong