Lu-Hung Chen, Ci-Ren Jiang
Functional principal component analysis is one the most commonly employed approaches in functional/longitudinal data analysis and we extend it to conduct $d$-dimensional functional/longitudinal data analysis. The computational issues emerging in the extension are fully addressed with our proposed solutions. The local linear smoothing technique is employed to perform estimation because of its capabilities of performing […]
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Yanping Huang, Sai Zhang
Deep learning methods have shown great promise in many practical applications, ranging from speech recognition, visual object recognition, to text processing. However, most of the current deep learning methods suffer from scalability problems for large-scale applications, forcing researchers or users to focus on small-scale problems with fewer parameters. In this paper, we consider a well-known […]
Yuxin Chen, David Keyes, Kody J.H. Law, Hatem Ltaief
This work considers black-box Bayesian inference over high-dimensional parameter spaces. The well-known adaptive Metropolis (AM) algorithm of (Haario etal. 2001) is extended herein to scale asymptotically uniformly with respect to the underlying parameter dimension for Gaussian targets, by respecting the variance of the target. The resulting algorithm, referred to as the dimension-independent adaptive Metropolis (DIAM) […]
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Quan Zhou, Wenlin Chen, Shiji Song, Jacob R. Gardner, Kilian Q. Weinberger, Yixin Chen
The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems […]
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Yan Zhou
The sequential Monte Carlo (smc) methods have been widely used for modern scientific computation. Bayesian model comparison has been successfully applied in many fields. Yet there have been few researches on the use of smc for the purpose of Bayesian model comparison. This thesis studies different smc strategies for Bayesian model computation. In addition, various […]
Andrew L. Beam, Sujit K. Ghosh, Jon Doyle
In recent years, the Hamiltonian Monte Carlo (HMC) algorithm has been found to work more efficiently compared to other popular Markov Chain Monte Carlo (MCMC) methods (such as random walk Metropolis-Hastings) in generating samples from a posterior distribution. A general framework for HMC based on the use of graphical processing units (GPUs) is shown to […]
Witold Andrzejewski, Artur Gramacki, Jaroslaw Gramacki
The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a […]
Jean-Baptiste Tristan, Daniel Huang, Joseph Tassarotti, Adam Pocock, Stephen J. Green, Guy L. Steele Jr
It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference procedure for it. For this approach to be practical, it is important to generate inference code that has reasonable performance. […]
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Alireza S. Mahani, Mansour T.A. Sharabiani
We present a single-chain parallelization strategy for Gibbs sampling of probabilistic Directed Acyclic Graphs, where contributions from child nodes to the conditional posterior distribution of a given node are calculated concurrently. For statistical models with many independent observations, such parallelism takes a Single-Instruction-Multiple-Data form, and can be efficiently implemented using multicore parallelization and vector instructions […]
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Robert B. Gramacy, Jarad Niemi, Robin Weiss
We explore how the big-three computing paradigms — symmetric multi-processor (SMC), graphical processing units (GPUs), and cluster computing — can together be brought to bare on large-data Gaussian processes (GP) regression problems via a careful implementation of a newly developed local approximation scheme. Our methodological contribution focuses primarily on GPU computation, as this requires the […]
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Yan Zhou
Sequential Monte Carlo is a family of algorithms for sampling from a sequence of distributions. Some of these algorithms, such as particle filters, are widely used in the physics and signal processing researches. More recent developments have established their application in more general inference problems such as Bayesian modeling. These algorithms have attracted considerable attentions […]
Lawrence M. Murray
LibBi is a software package for state-space modelling and Bayesian inference on modern computer hardware, including multi-core central processing units (CPUs), many-core graphics processing units (GPUs) and distributed-memory clusters of such devices. The software parses a domain-specific language for model specification, then optimises, generates, compiles and runs code for the given model, inference method and […]
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