Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components.We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplementalmaterials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Validation of ICDPIC software injury severity scores using a large regional trauma registry.

BACKGROUND: Administrative or quality improvement registries may or may not contain the elements needed for investigations by trauma researchers. International Classification of Diseases Program for Injury Categorisation (ICDPIC), a statistical program available through Stata, is a powerful tool that can extract injury severity scores from ICD-9-CM codes. We conducted a validation study for use of the ICDPIC in trauma research. METHODS: We conducted a retrospective cohort validation study of 40,418 patients with injury using a large regional trauma registry. ICDPIC-generated AIS scores for each body region were compared with trauma registry AIS scores (gold standard) in adult and paediatric populations. A separate analysis was conducted among patients with traumatic brain injury (TBI) comparing the ICDPIC tool with ICD-9-CM embedded severity codes. Performance in characterising overall injury severity, by the ISS, was also assessed. RESULTS: The ICDPIC tool generated substantial correlations in thoracic and abdominal trauma (weighted κ 0.87-0.92), and in head and neck trauma (weighted κ 0.76-0.83). The ICDPIC tool captured TBI severity better than ICD-9-CM code embedded severity and offered the advantage of generating a severity value for every patient (rather than having missing data). Its ability to produce an accurate severity score was consistent within each body region as well as overall. CONCLUSIONS: The ICDPIC tool performs well in classifying injury severity and is superior to ICD-9-CM embedded severity for TBI. Use of ICDPIC demonstrates substantial efficiency and may be a preferred tool in determining injury severity for large trauma datasets, provided researchers understand its limitations and take caution when examining smaller trauma datasets.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.