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Algorithms
Special Issues
Monte Carlo Methods and Algorithms
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Monte Carlo Methods and Algorithms

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (31 January 2018) | Viewed by 18740

Special Issue Editor

Prof. Dr. Faming Liang

E-Mail Website
Guest Editor
Department of Statistics, Purdue University, West Lafayette, IN 47906, USA
Interests: Monte carlo; big data; bioinformatics

Special Issue Information

Dear Colleagues,

The dramatic improvement in data collection and acquisition technologies in the past two decades has enabled scientists to collect vast amounts of data, such as climate data, omics data and credit card records. With growing size typically comes a growing complexity of data structures and of the models needed to account for the structures. Although Markov chain Monte Carlo has proven to be a powerful tool for analyzing the data of complex structures, its computer-intensive nature has limited its applications to big data problems. The objective of this special issue is to motivate developments of scalable Monte Carlo methods that address computational challenges in Bayesian analysis of big data. Topics of interest include (but are not limited to):

  • Distributed/parallel MCMC
  • MCMC using GPU computing
  • MCMC with split-and-merge strategies
  • Sequential Monte Carlo
  • Advantages of Bayesian Inference for Big Data
Prof. Dr. Faming Liang
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Monte Carlo
  • big data
  • bioinformatics

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Published Papers (3 papers)

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Research

20 pages, 1250 KiB  
Article
Locally Scaled and Stochastic Volatility Metropolis– Hastings Algorithms
by Wilson Tsakane Mongwe, Rendani Mbuvha and Tshilidzi Marwala
Algorithms 2021, 14(12), 351; https://doi.org/10.3390/a14120351 - 30 Nov 2021
Cited by 4 | Viewed by 2900
Abstract
Markov chain Monte Carlo (MCMC) techniques are usually used to infer model parameters when closed-form inference is not feasible, with one of the simplest MCMC methods being the random walk Metropolis–Hastings (MH) algorithm. The MH algorithm suffers from random walk behaviour, which results [...] Read more.
Markov chain Monte Carlo (MCMC) techniques are usually used to infer model parameters when closed-form inference is not feasible, with one of the simplest MCMC methods being the random walk Metropolis–Hastings (MH) algorithm. The MH algorithm suffers from random walk behaviour, which results in inefficient exploration of the target posterior distribution. This method has been improved upon, with algorithms such as Metropolis Adjusted Langevin Monte Carlo (MALA) and Hamiltonian Monte Carlo being examples of popular modifications to MH. In this work, we revisit the MH algorithm to reduce the autocorrelations in the generated samples without adding significant computational time. We present the: (1) Stochastic Volatility Metropolis–Hastings (SVMH) algorithm, which is based on using a random scaling matrix in the MH algorithm, and (2) Locally Scaled Metropolis–Hastings (LSMH) algorithm, in which the scaled matrix depends on the local geometry of the target distribution. For both these algorithms, the proposal distribution is still Gaussian centred at the current state. The empirical results show that these minor additions to the MH algorithm significantly improve the effective sample rates and predictive performance over the vanilla MH method. The SVMH algorithm produces similar effective sample sizes to the LSMH method, with SVMH outperforming LSMH on an execution time normalised effective sample size basis. The performance of the proposed methods is also compared to the MALA and the current state-of-art method being the No-U-Turn sampler (NUTS). The analysis is performed using a simulation study based on Neal’s funnel and multivariate Gaussian distributions and using real world data modeled using jump diffusion processes and Bayesian logistic regression. Although both MALA and NUTS outperform the proposed algorithms on an effective sample size basis, the SVMH algorithm has similar or better predictive performance when compared to MALA and NUTS across the various targets. In addition, the SVMH algorithm outperforms the other MCMC algorithms on a normalised effective sample size basis on the jump diffusion processes datasets. These results indicate the overall usefulness of the proposed algorithms. Full article
(This article belongs to the Special Issue Monte Carlo Methods and Algorithms)
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13 pages, 385 KiB  
Article
Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method
by Muneki Yasuda
Algorithms 2018, 11(4), 42; https://doi.org/10.3390/a11040042 - 4 Apr 2018
Cited by 6 | Viewed by 4919
Abstract
The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning [...] Read more.
The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning problems in the Boltzmann machine are NP-hard. The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning. In this paper, we study Boltzmann machine learning based on the (first-order) spatial Monte Carlo integration method, referred to as the 1-SMCI learning method, which was proposed in the author’s previous paper. In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE) method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is more effective than the MPLE. In the latter part, we compare the 1-SMCI learning method with other effective methods, ratio matching and minimum probability flow, using a numerical experiment, and show the 1-SMCI learning method outperforms them. Full article
(This article belongs to the Special Issue Monte Carlo Methods and Algorithms)
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23 pages, 593 KiB  
Article
Generalized Kinetic Monte Carlo Framework for Organic Electronics
by Waldemar Kaiser, Johannes Popp, Michael Rinderle, Tim Albes and Alessio Gagliardi
Algorithms 2018, 11(4), 37; https://doi.org/10.3390/a11040037 - 26 Mar 2018
Cited by 36 | Viewed by 10212
Abstract
In this paper, we present our generalized kinetic Monte Carlo (kMC) framework for the simulation of organic semiconductors and electronic devices such as solar cells (OSCs) and light-emitting diodes (OLEDs). Our model generalizes the geometrical representation of the multifaceted properties of the organic [...] Read more.
In this paper, we present our generalized kinetic Monte Carlo (kMC) framework for the simulation of organic semiconductors and electronic devices such as solar cells (OSCs) and light-emitting diodes (OLEDs). Our model generalizes the geometrical representation of the multifaceted properties of the organic material by the use of a non-cubic, generalized Voronoi tessellation and a model that connects sites to polymer chains. Herewith, we obtain a realistic model for both amorphous and crystalline domains of small molecules and polymers. Furthermore, we generalize the excitonic processes and include triplet exciton dynamics, which allows an enhanced investigation of OSCs and OLEDs. We outline the developed methods of our generalized kMC framework and give two exemplary studies of electrical and optical properties inside an organic semiconductor. Full article
(This article belongs to the Special Issue Monte Carlo Methods and Algorithms)
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