Parallel Fast Gauss Transform

Sampath, Rahul S.; Sundar, Hari; Veerapaneni, Shravan

doi:10.1109/sc.2010.39

Cited by 19 publications

(13 citation statements)

References 26 publications

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“…We used ε = 0.1 and decreased the bandwidth parameter h as more cores are added to keep the number of distance computations constant per core; a similar experiment setup was used in ref. 47, though we plan to perform more thorough evaluations. The timings for the computation maintains around 60% parallel efficiency above 96 cores.…”

Section: Resultsmentioning

confidence: 99%

A distributed kernel summation framework for general‐dimension machine learning

Lee

Sao

Vuduc

et al. 2013

Statistical Analysis

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Kernel summations are a ubiquitous key computational bottleneck in many data analysis methods. In this paper, we attempt to marry, for the first time, the best relevant techniques in parallel computing, where kernel summations are in low dimensions, with the best general‐dimension algorithms from the machine learning literature. We provide the first distributed implementation of kernel summation framework that can utilize: (i) various types of deterministic and probabilistic approximations that may be suitable for low and high‐dimensional problems with a large number of data points; (ii) any multidimensional binary tree using both distributed memory and shared memory parallelism; and (iii) a dynamic load balancing scheme to adjust work imbalances during the computation. Our hybrid message passing interface (MPI)/OpenMP codebase has wide applicability in providing a general framework to accelerate the computation of many popular machine learning methods. Our experiments show scalability results for kernel density estimation on a synthetic ten‐dimensional dataset containing over one billion points and a subset of the Sloan Digital Sky Survey Data up to 6144 cores. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013

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Section: Resultsmentioning

confidence: 99%

A distributed kernel summation framework for general‐dimension machine learning

Lee

Sao

Vuduc

et al. 2013

Statistical Analysis

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“…Notable examples are the least-squares' approach ( [43,57]), the quantization approach and the Malliavin calculus based formulation (see [13] for a thorough comparison and improvements of these techniques). In the spirit of [17], one may also consider non-parametric regression (see [38] and [56]) combined with speeding up techniques like Kd-trees ( [32,40]) or the Fast Gauss Transform ( [61,47,50,54,51]) in the case of kernel regression.…”

Section: Outline Of the Solutionmentioning

confidence: 99%

A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension

Aïd¹,

Campi²,

Langrené³

et al. 2014

SIAM J. Finan. Math.

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In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the regression basis used to approximate conditional expectations, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants in dimension eight, i.e. with two di erent technologies and six random factors.

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“…We used = 0.1 and decreased the bandwidth parameter h as more cores are added to keep the number of distance computations constant per core; a similar experiment setup was used in ref. 47, though we plan to perform more thorough evaluations. The timings for the computation maintains around 60% parallel efficiency above 96 cores.…”

Section: Scalability Of Kernel Summationmentioning

confidence: 99%

A Distributed Kernel Summation Framework for General-Dimension Machine Learning

Lee

Vuduc

Gray

2012

Proceedings of the 2012 SIAM International Conference on Data Mining

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Kernel summations are a ubiquitous key computational bottleneck in many data analysis methods. In this paper, we attempt to marry, for the first time, the best relevant techniques in parallel computing, where kernel summations are in low dimensions, with the best general-dimension algorithms from the machine learning literature. We provide the first distributed implementation of kernel summation framework that can utilize: (i) various types of deterministic and probabilistic approximations that may be suitable for low and high-dimensional problems with a large number of data points; (ii) any multidimensional binary tree using both distributed memory and shared memory parallelism; and (iii) a dynamic load balancing scheme to adjust work imbalances during the computation. Our hybrid message passing interface (MPI)/OpenMP codebase has wide applicability in providing a general framework to accelerate the computation of many popular machine learning methods. Our experiments show scalability results for kernel density estimation on a synthetic ten-dimensional dataset containing over one billion points and a subset of the Sloan Digital Sky Survey Data up to 6144 cores.

show abstract

Parallel Fast Gauss Transform

Cited by 19 publications

References 26 publications

A distributed kernel summation framework for general‐dimension machine learning

A distributed kernel summation framework for general‐dimension machine learning

A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension

A Distributed Kernel Summation Framework for General-Dimension Machine Learning

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