179,065 research outputs found

    High-dimensional classification using features annealed independence rules

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    Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is poorly understood. In a seminal paper, Bickel and Levina [Bernoulli 10 (2004) 989--1010] show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that even for the independence classification rule, classification using all the features can be as poor as the random guessing due to noise accumulation in estimating population centroids in high-dimensional feature space. In fact, we demonstrate further that almost all linear discriminants can perform as poorly as the random guessing. Thus, it is important to select a subset of important features for high-dimensional classification, resulting in Features Annealed Independence Rules (FAIR). The conditions under which all the important features can be selected by the two-sample tt-statistic are established. The choice of the optimal number of features, or equivalently, the threshold value of the test statistics are proposed based on an upper bound of the classification error. Simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure.Comment: Published in at http://dx.doi.org/10.1214/07-AOS504 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

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    As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.Comment: 8 pages, 0 figure

    Wasserstein Introspective Neural Networks

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    We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing INN's generative modeling capability. WINN has three interesting properties: (1) A mathematical connection between the formulation of the INN algorithm and that of Wasserstein generative adversarial networks (WGAN) is made. (2) The explicit adoption of the Wasserstein distance into INN results in a large enhancement to INN, achieving compelling results even with a single classifier --- e.g., providing nearly a 20 times reduction in model size over INN for unsupervised generative modeling. (3) When applied to supervised classification, WINN also gives rise to improved robustness against adversarial examples in terms of the error reduction. In the experiments, we report encouraging results on unsupervised learning problems including texture, face, and object modeling, as well as a supervised classification task against adversarial attacks.Comment: Accepted to CVPR 2018 (Oral

    El Niño-related summer precipitation anomalies in Southeast Asia modulated by the Atlantic multidecadal oscillation

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    AbstractHow the Atlantic Multidecadal Oscillation (AMO) affects El Niño-related signals in Southeast Asia is investigated in this study on a subseasonal scale. Based on observational and reanalysis data, as well as numerical model simulations, El Niño-related precipitation anomalies are analyzed for AMO positive and negative phases, which reveals a time-dependent modulation of the AMO: (i) In May?June, the AMO influences the precipitation in Southern China (SC) and the Indochina peninsula (ICP) by modulating the El Niño-related air-sea interaction over the western North Pacific (WNP). During negative AMO phases, cold sea surface temperature anomalies (SSTAs) over the WNP favor the maintaining of the WNP anomalous anticyclone (WNPAC). The associated southerly (westerly) anomalies on the northwest (southwest) flank of the WNPAC enhance (reduce) the climatological moisture transport to SC (the ICP) and result in wetter (drier) than normal conditions. In contrast, during positive AMO phases, weak SSTAs over the WNP lead to limited influence of El Niño on precipitation in Southeast Asia. (ii) In July?August, the teleconnection impact from the North Atlantic is more manifest than that in May?June. During positive AMO phases, the warmer than normal North Atlantic favors anomalous wave trains, which propagate along the ?great circle route? and result in positive pressure anomalies over SC, consequently suppressing precipitation in SC and the ICP. During negative AMO phases, the anomalous wave trains tend to propagate eastward from Europe to Northeast Asia along the summer Asian jet, exerting limited influence on Southeast Asia