SCOPE: Scalable Composite Optimization for Learning on Spark

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods are not scalable enough. In this paper, we propose a novel DSO method, called \underline{s}calable \underline{c}omposite \underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods

Impacts of DEM resolution and area threshold value uncertainty on the drainage network derived using SWAT

Many hydrological algorithms have been developed to automatically extract drainage networks from DEM, and the D8 algorithm is widely used worldwide to delineate drainage networks and catchments. The simulation accuracy of the SWAT model depends on characteristics of the watershed, and previous studies of DEM resolution and its impacts on drainage network extraction have not generally considered the effects of resolution and threshold value on uncertainty. In order to assess the influence of different DEM resolutions and drainage threshold values on drainage network extraction using the SWAT model, 10 basic watershed regions in China were chosen as case studies to analyse the relationship between extracted watershed parameters and the threshold value. SRTM DEM data at 3 different resolutions were used in this study, and regression analysis for DEM resolution, threshold value and extraction effects was done. The results show that DEM resolution influences the selected flow accumulation threshold value; the suitable flow accumulation threshold value increases as the DEM resolution increases, and shows greater variability for basins with lower drainage densities. The link between drainage area threshold value and stream network extraction results was also examined, and showed a variation trend of power function y = axb between the sub-basin counts and threshold value, i.e., the maximum reach length increases while the threshold value increases, and the minimum reach length shows no relation with the threshold value. The stream network extraction resulting from a 250 m DEM resolution and a 50 000 ha threshold value was similar to the real stream network. The drainage network density and the threshold value also shows a trend of power function y = axb ; the value of b is usually 0.5.Keywords: SWAT, digital elevation model (DEM), watershed delineation, threshold valu

Deep Generative Models on 3D Representations: A Survey

Generative models, as an important family of statistical modeling, target learning the observed data distribution via generating new instances. Along with the rise of neural networks, deep generative models, such as variational autoencoders (VAEs) and generative adversarial network (GANs), have made tremendous progress in 2D image synthesis. Recently, researchers switch their attentions from the 2D space to the 3D space considering that 3D data better aligns with our physical world and hence enjoys great potential in practice. However, unlike a 2D image, which owns an efficient representation (i.e., pixel grid) by nature, representing 3D data could face far more challenges. Concretely, we would expect an ideal 3D representation to be capable enough to model shapes and appearances in details, and to be highly efficient so as to model high-resolution data with fast speed and low memory cost. However, existing 3D representations, such as point clouds, meshes, and recent neural fields, usually fail to meet the above requirements simultaneously. In this survey, we make a thorough review of the development of 3D generation, including 3D shape generation and 3D-aware image synthesis, from the perspectives of both algorithms and more importantly representations. We hope that our discussion could help the community track the evolution of this field and further spark some innovative ideas to advance this challenging task