Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior performance. As an extreme, but not uncommon, example use of the wrong hyperparameter priors can even lead to impropriety of the posterior. For exchangeable hierarchical multivariate normal models, we first determine when a standard class of hierarchical priors results in proper or improper posteriors. We next determine which elements of this class lead to admissible estimators of the mean under quadratic loss; such considerations provide one useful guideline for choice among hierarchical priors. Finally, computational issues with the resulting posterior distributions are addressed.Comment: Published at http://dx.doi.org/10.1214/009053605000000075 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A High-Throughput Solver for Marginalized Graph Kernels on GPU

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned conjugate gradient (PCG) method to compute the solution to a generalized Laplacian equation associated with the tensor product of two graphs. To cope with the gap between the instruction throughput and the memory bandwidth of current generation GPUs, our solver forms the tensor product linear system on-the-fly without storing it in memory when performing matrix-vector dot product operations in PCG. Such on-the-fly computation is accomplished by using threads in a warp to cooperatively stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. Besides, we propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to improve the efficiency of the sparse format.We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales

Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant Symmetry in QED''

We show that recently found symmetries in QED are just non-local versions of standard BRST symmetry.Comment: 4 pages, revte

RGB-D-based Action Recognition Datasets: A Survey

Human action recognition from RGB-D (Red, Green, Blue and Depth) data has attracted increasing attention since the first work reported in 2010. Over this period, many benchmark datasets have been created to facilitate the development and evaluation of new algorithms. This raises the question of which dataset to select and how to use it in providing a fair and objective comparative evaluation against state-of-the-art methods. To address this issue, this paper provides a comprehensive review of the most commonly used action recognition related RGB-D video datasets, including 27 single-view datasets, 10 multi-view datasets, and 7 multi-person datasets. The detailed information and analysis of these datasets is a useful resource in guiding insightful selection of datasets for future research. In addition, the issues with current algorithm evaluation vis-\'{a}-vis limitations of the available datasets and evaluation protocols are also highlighted; resulting in a number of recommendations for collection of new datasets and use of evaluation protocols

Estimation of the Kronecker Covariance Model by Quadratic Form

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to th

Analysis of complex contagions in random multiplex networks

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold \tau. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ links will turn active if $\sum{c_i m_i}/\sum{c_i k_i}$ exceeds its threshold \tau. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure

Risk evaluation for production-injection recompletion and sidetrack

Using a decision tree and stochastic parameters, expected monetary value is calculated to evaluate optimal sidetrack time. In view of placing a high confidence level on analytical approach to optimal sidetrack time for a waterflooded reservoir based on possible uncertainty of economic and reservoir parameters and probability of sidetrack success, a major assumption on a parameter in a previous study is re-evaluated. Material balance and displacement efficiency are used to re-evaluate this critical waterflood performance parameter. The change in the relative influence of the stochastic parameters to optimal sidetrack time due to re-evaluation calls for much attention with probable need to further reduce assumptions made, however insignificant the parameter may be. This change will affect the degree of acceptability of the analytical approach. The probability of success of sidetrack sums up the geological and technical uncertainties, deconvolution of these will give the analytical approach an edge