Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related variable screening procedures are proposed. Under the nonparametric additive models, it is shown that under some mild technical conditions, the proposed independence screening methods enjoy a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, an iterative nonparametric independence screening (INIS) is also proposed to enhance the finite sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.Comment: 48 page

Richly Activated Graph Convolutional Network for Action Recognition with Incomplete Skeletons

Current methods for skeleton-based human action recognition usually work with completely observed skeletons. However, in real scenarios, it is prone to capture incomplete and noisy skeletons, which will deteriorate the performance of traditional models. To enhance the robustness of action recognition models to incomplete skeletons, we propose a multi-stream graph convolutional network (GCN) for exploring sufficient discriminative features distributed over all skeleton joints. Here, each stream of the network is only responsible for learning features from currently unactivated joints, which are distinguished by the class activation maps (CAM) obtained by preceding streams, so that the activated joints of the proposed method are obviously more than traditional methods. Thus, the proposed method is termed richly activated GCN (RA-GCN), where the richly discovered features will improve the robustness of the model. Compared to the state-of-the-art methods, the RA-GCN achieves comparable performance on the NTU RGB+D dataset. Moreover, on a synthetic occlusion dataset, the performance deterioration can be alleviated by the RA-GCN significantly.Comment: Accepted by ICIP 2019, 5 pages, 3 figures, 3 table

Combining Local Appearance and Holistic View: Dual-Source Deep Neural Networks for Human Pose Estimation

We propose a new learning-based method for estimating 2D human pose from a single image, using Dual-Source Deep Convolutional Neural Networks (DS-CNN). Recently, many methods have been developed to estimate human pose by using pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective. In this paper, we propose to integrate both the local (body) part appearance and the holistic view of each local part for more accurate human pose estimation. Specifically, the proposed DS-CNN takes a set of image patches (category-independent object proposals for training and multi-scale sliding windows for testing) as the input and then learns the appearance of each local part by considering their holistic views in the full body. Using DS-CNN, we achieve both joint detection, which determines whether an image patch contains a body joint, and joint localization, which finds the exact location of the joint in the image patch. Finally, we develop an algorithm to combine these joint detection/localization results from all the image patches for estimating the human pose. The experimental results show the effectiveness of the proposed method by comparing to the state-of-the-art human-pose estimation methods based on pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective.Comment: CVPR 201

Merging Rates of the First Objects and the Formation of First Mini-Filaments in Models with Massive Neutrinos

We study the effect of massive neutrinos on the formation and evolution of the first filaments containing the first star-forming halos of mass M~10^{6}M_sun at z~20. With the help of the extended Press-Schechter formalism, we evaluate analytically the rates of merging of the first star-forming halos into zero-dimensional larger halos and one-dimensional first filaments. It is shown that as the neutrino mass fraction f_{\nu} increases, the halo-to-filament merging rate increases while the halo-to-halo merging rate decreases sharply. For f_{\nu}<=0.04, the halo-to-filament merging rate is negligibly low at all filament mass scales, while for f_{\nu}>=0.07 the halo-to-filament merging rate exceeds 0.1 at the characteristic filament mass scale of ~10^{9}M_sun. The distribution of the redshifts at which the first filaments ultimately collapse along their longest axes is derived and found to have a sharp maximum at z~8. We also investigate the formation and evolution of the second generation filaments which contain the first galaxies of mass 10^{9}M_sun at z=8 as the parent of the first generation filaments. A similar trend is found: For f_{\nu}>= 0.07 the rate of clustering of the first galaxies into the second-generation filaments exceeds 0.3 at the characteristic mass scale of ~10^{11}M_sun. The longest-axis collapse of these second-generation filaments are found to occur at z~3. The implications of our results on the formation of massive high-z galaxies and the early metal enrichment of the intergalactic media by supernova-driven outflows, and possibility of constraining the neutrino mass from the mass distribution of the high-z central blackholes are discussed.Comment: Accepted for publication in ApJ, mistakes in the calculation of the merging rates corrected, feasibility study of constraining neutrino mass with high-z quasar luminosity function presented, discussion improved, 7 figure