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Optimal Poisson Subsampling for Softmax Regression

系统科学与复杂性学报:英文版 2023年第4期36卷 1609-1625页

作者： YAO Yaqiong ZOU Jiahui WANG Haiying Department of Statistics University of ConnecticutStorrsCT06269USA School of Statistics Capital University of Economics and BusinessBeijing 100070China

Softmax regression,which is also called multinomial logistic regression,is widely used in various fields for modeling the relationship between covariates and categorical responses with multiple *** increasing volumes of data bring new challenges for parameter estimation in softmax regression,and the optimal subsampling method is an effective way to solve ***,optimal subsampling with replacement requires to access all the sampling probabilities simultaneously to draw a subsample,and the resultant subsample could contain duplicate *** this paper,the authors consider Poisson subsampling for its higher estimation accuracy and applicability in the scenario that the data exceed the memory *** authors derive the asymptotic properties of the general Poisson subsampling estimator and obtain optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under both A-and L-optimality *** optimal subsampling probabilities contain unknown quantities from the full dataset,so the authors suggest an approximately optimal Poisson subsampling algorithm which contains two sampling steps,with the first step as a pilot *** authors demonstrate the performance of our optimal Poisson subsampling algorithm through numerical simulations and real data examples.

关键词： Multinomial logistic regression optimality criterion optimal subsampling

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Bats and marsupials as indicators of endemism in the Yungas forest of Argentina

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Zoological Research 2010年第6期31卷 633-644页

作者： María L Sandoval Claudia A Szumik Rubén M Barquez PIDBA (Research Program of Argentinean Biodiversity) Natural Sciences Faculty and Miguel Lillo Institute National University of Tucuman Miguel Lillo 205 San Miguel de Tucumán CP 4000 Tucumán Argentina CONICET (National Council of Scientific and Technical Researches) Argentina INSUE (Superior Institute of Entomology "Dr. Abraham Willink") Natural Sciences Faculty and Miguel Lillo Institute National University of Tucuman Miguel Lillo 205 San Miguel de Tucumán CP 4000 Tucumán Argentina

Several studies have characterized the Yungas as a separate biogeographic unit, mainly based in floristic components. However, these characterizations were mainly qualitative and did not include faunal groups. The Yungas have been assumed as a region with rich floral and faunal diversity, but without testing how well they are described by animal distributions. Our study consists of a formal analysis of endemism based on distribution of small mammals in the southernmost portion of the Yungas. This area is biogeographically very interesting because the Yungas are comprised of discontinuous fragments of forests that extend into temperate arid and semiarid habitats. As a first approximation, we contrasted a group of volant species （bats） versus a group of non-volant species （marsupials）. Our results show that small mammals are efficient indicators of endemism in Yungas. Eighty percent of the species of small marsupials included in the analysis supported the identified areas as being zones of endemism. Regarding bats, almost 55 percent of the species supported a designation of endemism. The results also show that the areas we considered are congruent with the botanical definition of the Yungas of northwestern Argentina and their subdivisions, an assumption that had not been previously tested with a formal quantitative method. We also found that non-volant species are better indicators of endemism than volant ones at regional scales, but volant species are better indicators than was previously thought.

关键词： Andean rainforests Chiroptera Didelphimorphia optimality criterion Small mammals

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