Model Selection for High Dimensional Quadratic Regression via Regularization

Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects and interaction effects. Existing regularization methods generally achieve this goal by solving complex optimization problems, which usually demands high computational cost and hence are not feasible for high dimensional data. This paper focuses on scalable regularization methods for model selection in high dimensional QR. We first consider two-stage regularization methods and establish theoretical properties of the two-stage LASSO. Then, a new regularization method, called Regularization Algorithm under Marginality Principle (RAMP), is proposed to compute a hierarchy-preserving regularization solution path efficiently. Both methods are further extended to solve generalized QR models. Numerical results are also shown to demonstrate performance of the methods.Comment: 37 pages, 1 figure with supplementary materia

Pulsar interpretation of the lepton spectra measured by AMS-02

AMS-02 recently published its lepton spectra measurement. The results show that the positron fraction no longer increases above $\sim$200 GeV. The aim of this work is to investigate the possibility that the excess of positron fraction is due to pulsars. Nearby known pulsars from ATNF catalogue are considered as a possible primary positron source of the high energy positrons. We find that the pulsars with age $T\simeq (0.45\sim4.5)\times10^{5}$ yr and distance $d<0.5$ kpc can explain the behavior of positron fraction of AMS-02 in the range of high energy. We show that each of the four pulsars --- Geminga, J1741-2054, Monogem and J0942-5552 --- is able to be a single source satisfying all considered physical requirements. We also discuss the possibility that these high energy $e^{\pm}$ are from multiple pulsars. The multiple pulsars contribution predicts a positron fraction with some structures at higher energies.Comment: 27 pages, 5 figures, 3 tables, accepted for publication in EPJ

School Quality and Housing Prices: Empirical Evidence Based on a Natural Experiment in Shanghai, China

The extent to which the quantity and quality of education is capitalized into housing prices is a key issue in understanding the relationship between allocation of educational resources and the housing market. Using monthly panel data of 52 residential areas in Shanghai and employing a natural experiment of designating Shanghai Experimental Model Senior High Schools (EMSHS), we find that housing prices in Shanghai have capitalized the access to quality schools and other public goods. One quality school per square kilometer raises average housing prices by approximately 19%, and one best EMSHS per square kilometer increases housing prices by 21%. We also match the schools designated for EMSHS with schools of similar quality but not designated for EMSHS, and compare housing prices in the corresponding areas. We find that the designation increased the housing prices, showing that dissemination of information about school quality was significantly affected by the designation.education, housing market, capitalization, public goods, natural experiment

Long Short-Term Memory Spatial Transformer Network

Spatial transformer network has been used in a layered form in conjunction with a convolutional network to enable the model to transform data spatially. In this paper, we propose a combined spatial transformer network (STN) and a Long Short-Term Memory network (LSTM) to classify digits in sequences formed by MINST elements. This LSTM-STN model has a top-down attention mechanism profit from LSTM layer, so that the STN layer can perform short-term independent elements for the statement in the process of spatial transformation, thus avoiding the distortion that may be caused when the entire sequence is spatially transformed. It also avoids the influence of this distortion on the subsequent classification process using convolutional neural networks and achieves a single digit error of 1.6\% compared with 2.2\% of Convolutional Neural Network with STN layer