Dropout and other feature noising schemes have shown promise in controlling over-fitting by artificially corrupting the training data. Though extensive studies have been performed for generalized linear models, little...Dropout and other feature noising schemes have shown promise in controlling over-fitting by artificially corrupting the training data. Though extensive studies have been performed for generalized linear models, little has been done for support vector machines （SVMs）, one of the most successful approaches for supervised learning. This paper presents dropout training for both linear SVMs and the nonlinear extension with latent representation learning. For linear SVMs, to deal with the intractable expectation of the non-smooth hinge loss under corrupting distributions, we develop an iteratively re-weighted least square （IRLS） algorithm by exploring data augmentation techniques. Our algorithm iteratively minimizes the expectation of a re- weighted least square problem, where the re-weights are analytically updated. For nonlinear latent SVMs, we con- sider learning one layer of latent representations in SVMs and extend the data augmentation technique in conjunction with first-order Taylor-expansion to deal with the intractable expected hinge loss and the nonlinearity of latent representa- tions. Finally, we apply the similar data augmentation ideas to develop a new IRLS algorithm for the expected logistic loss under corrupting distributions, and we further develop a non-linear extension of logistic regression by incorporating one layer of latent representations. Our algorithms offer insights on the connection and difference between the hinge loss and logistic loss in dropout training. Empirical results on several real datasets demonstrate the effectiveness of dropout training on significantly boosting the classification accuracy of both linear and nonlinear SVMs.展开更多
We have obtained deep J and Ks-band images centered on a bright radio quiet QSO UM 402 （Zem = 2.856） using the IRCS camera and adaptive optics systems that are part of the Subaru Telescope, as well as retrieved WFC3...We have obtained deep J and Ks-band images centered on a bright radio quiet QSO UM 402 （Zem = 2.856） using the IRCS camera and adaptive optics systems that are part of the Subaru Telescope, as well as retrieved WFC3/F140W archive images of this object. A faint galaxy （ink = 23.32 ±0.05 in the Vega magnitude system） that lies ～2.4″north of the QSO sightline has been clearly resolved in all three deep high resolution datasets, and appears as an irregular galaxy with two close components in the Ks-band images （separation ～ 0.31″）. Given the small impact parameter （b = 19.6 kpc, at Zlls = 2.531）, as well as the red color of （J - Ks）vega ～1.6, it might be a candidate galaxy giving rise to the Lyman Limit system absorption at Zabs = 2.531 seen in the QSO spectrum. After carefully subtracting the point spread function from the QSO images, the host galaxy of this bright radio quiet QSO at z ～ 3 was marginally revealed. We placed a lower limit on the host component of mk～ 23.3 according to our analyses.展开更多
A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The governing thermomechanical equations consist of the three-dimensional full-S...A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The governing thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.展开更多
文摘Dropout and other feature noising schemes have shown promise in controlling over-fitting by artificially corrupting the training data. Though extensive studies have been performed for generalized linear models, little has been done for support vector machines （SVMs）, one of the most successful approaches for supervised learning. This paper presents dropout training for both linear SVMs and the nonlinear extension with latent representation learning. For linear SVMs, to deal with the intractable expectation of the non-smooth hinge loss under corrupting distributions, we develop an iteratively re-weighted least square （IRLS） algorithm by exploring data augmentation techniques. Our algorithm iteratively minimizes the expectation of a re- weighted least square problem, where the re-weights are analytically updated. For nonlinear latent SVMs, we con- sider learning one layer of latent representations in SVMs and extend the data augmentation technique in conjunction with first-order Taylor-expansion to deal with the intractable expected hinge loss and the nonlinearity of latent representa- tions. Finally, we apply the similar data augmentation ideas to develop a new IRLS algorithm for the expected logistic loss under corrupting distributions, and we further develop a non-linear extension of logistic regression by incorporating one layer of latent representations. Our algorithms offer insights on the connection and difference between the hinge loss and logistic loss in dropout training. Empirical results on several real datasets demonstrate the effectiveness of dropout training on significantly boosting the classification accuracy of both linear and nonlinear SVMs.
基金Supported by the National Natural Science Foundation of China
文摘We have obtained deep J and Ks-band images centered on a bright radio quiet QSO UM 402 （Zem = 2.856） using the IRCS camera and adaptive optics systems that are part of the Subaru Telescope, as well as retrieved WFC3/F140W archive images of this object. A faint galaxy （ink = 23.32 ±0.05 in the Vega magnitude system） that lies ～2.4″north of the QSO sightline has been clearly resolved in all three deep high resolution datasets, and appears as an irregular galaxy with two close components in the Ks-band images （separation ～ 0.31″）. Given the small impact parameter （b = 19.6 kpc, at Zlls = 2.531）, as well as the red color of （J - Ks）vega ～1.6, it might be a candidate galaxy giving rise to the Lyman Limit system absorption at Zabs = 2.531 seen in the QSO spectrum. After carefully subtracting the point spread function from the QSO images, the host galaxy of this bright radio quiet QSO at z ～ 3 was marginally revealed. We placed a lower limit on the host component of mk～ 23.3 according to our analyses.
基金the US DOE Office of Science’s Climate Change Prediction Program through DE-FG02-07ER64431,DE-FG02-07ER64432 and DOE 07SCPF152the US National Science Foundation under grant number DMS-0913491.
文摘A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The governing thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.
