The growth in the use of computationally intensive statistical procedures, especially with Big Data, has necessitated the usage of parallel computation on diverse platforms such as multicore, GPU, clusters and clouds. However, slowdown due to interprocess communication costs typically limits such methods to "embarrassingly parallel" (EP) algorithms, especially on non-shared memory platforms. This paper develops a broadly-applicable method for converting many non-EP algorithms into statistically equivalent EP ones. The method is shown to yield excellent levels of speedup for a variety of statistical computations. It also overcomes certain problems of memory limitations.
@cite_0 developed a bootstrap approach related to CA, based on applying the bootstrap method to a number of small random subsamples of the original data. Since any bootstrap method requires the user to choose the values of hyperparameters''---size and numbers of subsamples---the authors proposed an adaptive method to choose these parameters. They derived some asymptotic results, but also noted that their method will fail in settings in which the ordinary bootstrap fails. On the other hand, they indicated how their method can be used for time series data, something other CA methods have not yet been extended to.
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It is a common practice to use resampling methods such as the bootstrap for calculating the p-value for each test when performing large scale multiple testing. The precision of the bootstrap p-values and that of the false discovery rate (FDR) relies on the number of bootstraps used for testing each hypothesis. Clearly, the larger the number of bootstraps the better the precision. However, the required number of bootstraps can be computationally burdensome, and it multiplies the number of tests to be performed. Further adding to the computational challenge is that in some applications the calculation of the test statistic itself may require considerable computation time. As technology improves one can expect the dimension of the problem to increase as well. For instance, during the early days of microarray technology, the number of probes on a cDNA chip was less than 10,000. Now the Affymetrix chips come with over 50,000 probes per chip. Motivated by this important need, we developed a simple adaptive bootstrap methodology for large scale multiple testing, which reduces the total number of bootstrap calculations while ensuring the control of the FDR. The proposed algorithm results in a substantial reduction in the number of bootstrap samples. Based on a simulation study we found that, relative to the number of bootstraps required for the Benjamini-Hochberg (BH) procedure, the standard FDR methodology which was the proposed methodology achieved a very substantial reduction in the number of bootstraps. In some cases the new algorithm required as little as 1 6th the number of bootstraps as the conventional BH procedure. Thus, if the conventional BH procedure used 1,000 bootstraps, then the proposed method required only 160 bootstraps. This methodology has been implemented for time-course dose-response data in our software, ORIOGEN, which is available from the authors upon request. Hyperparameter tuning is often done manually but current research has proven that automatic tuning yields effective hyperparameter configurations even faster and does not require any expertise. To further improve the search, recent publications propose transferring knowledge from previous experiments to new experiments. We adapt the sequential model-based optimization by replacing its surrogate model and acquisition function with one policy that is optimized for the task of hyperparameter tuning. This policy generalizes over previous experiments but neither uses a model nor uses meta-features, nevertheless, outperforms the state of the art. We show that a static ranking of hyperparameter combinations yields competitive results and substantially outperforms a random hyperparameter search. Thus, it is a fast and easy alternative to complex hyperparameter tuning strategies and allows practitioners to tune their hyperparameters by simply using a look-up table. We made look-up tables for two classifiers publicly available: SVM and AdaBoost. Furthermore, we propose a similarity measure for data sets that yields more comprehensible results than those using meta-features. We show how this similarity measure can be applied to surrogate models in the SMBO framework and empirically show that this change leads to better hyperparameter configurations in less trials. In this paper, we tackle the problem of constructing a differentially private synopsis for two-dimensional datasets such as geospatial datasets. The current state-of-the-art methods work by performing recursive binary partitioning of the data domains, and constructing a hierarchy of partitions. We show that the key challenge in partition-based synopsis methods lies in choosing the right partition granularity to balance the noise error and the non-uniformity error. We study the uniform-grid approach, which applies an equi-width grid of a certain size over the data domain and then issues independent count queries on the grid cells. This method has received no attention in the literature, probably due to the fact that no good method for choosing a grid size was known. Based on an analysis of the two kinds of errors, we propose a method for choosing the grid size. Experimental results validate our method, and show that this approach performs as well as, and often times better than, the state-of-the-art methods. We further introduce a novel adaptive-grid method. The adaptive grid method lays a coarse-grained grid over the dataset, and then further partitions each cell according to its noisy count. Both levels of partitions are then used in answering queries over the dataset. This method exploits the need to have finer granularity partitioning over dense regions and, at the same time, coarse partitioning over sparse regions. Through extensive experiments on real-world datasets, we show that this approach consistently and significantly outperforms the uniform-grid method and other state-of-the-art methods. In this paper, we tackle the problem of constructing a differentially private synopsis for two-dimensional datasets such as geospatial datasets. The current state-of-the-art methods work by performing recursive binary partitioning of the data domains, and constructing a hierarchy of partitions. We show that the key challenge in partition-based synopsis methods lies in choosing the right partition granularity to balance the noise error and the non-uniformity error. We study the uniform-grid approach, which applies an equi-width grid of a certain size over the data domain and then issues independent count queries on the grid cells. This method has received no attention in the literature, probably due to the fact that no good method for choosing a grid size was known. Based on an analysis of the two kinds of errors, we propose a method for choosing the grid size. Experimental results validate our method, and show that this approach performs as well as, and often times better than, the state-of-the-art methods. We further introduce a novel adaptive-grid method. The adaptive grid method lays a coarse-grained grid over the dataset, and then further partitions each cell according to its noisy count. Both levels of partitions are then used in answering queries over the dataset. This method exploits the need to have finer granularity partitioning over dense regions and, at the same time, coarse partitioning over sparse regions. Through extensive experiments on real-world datasets, we show that this approach consistently and significantly outperforms the uniform-grid method and other state-of-the-art methods.